SharePrint

# Number Theory Part 2?

## Http://answers.yahoo.com/question/index;_ylt=AoQG_NuxMjZwzAIa9N1OJ67sy6IX;_ylv=3?qid=20080618132109AATgA4G Are there more answers other than (a,b,k) = (34,13,1425)? If so, you should have noticed that k is a multiple of 3. Prove this is true and show me how you reached your answers. If not, give a proof to why no more solutions exist. Enjoy.

Can't provide a proof, but using the computer for a and b,
each up to 1000, I obtained these four solutions -
EDIT: Sorry, first said a million, but it was only a thousand.

(a, b, k) =

(13, 5, 231) .......... k = 3 * 77

(34, 13, 1425) .......... k = 3 * 475

(233, 89, 62907) .......... k = 3 * 20969

(610, 233, 428217) .......... k = 3 * 142739

Still looking into it!!!

EDIT 1:
I seem to have detected a pattern in Fibonacci numbers -
check out the values of a and b.

Must look into that more closely, but for now, I have these
equations for a, b and k, each dependent on 'n' only,
for n = 1, 2, 3, ...

a = 89n^2 - 246n + 170
b = 34x^2 - 94n + 65
k = 233n^2 - 644n + 442

If everything is going smoothly there, it appears
there may be an infinite number of solutions.

EDIT 2:
Oh! Drat!, we ran out of Fibonacci numbers at n = 5.

But I think my equations are at fault, because the
pattern of Fibonacci numbers does seem to hold.

For a = 4181 and b = 1597, k = 20043711.
For a = 10946 and b = 4181, k = 137328513.

I'll have another go.

EDIT 3 :
So if the Fibonacci numbers are :
F(0) = 0, F(1) = 1, F(2) = 1, F(3) = 2, ..., then it
appears that there may be two patterns for a and b :

First pattern :
a = F(7) and b = F(5)
a = F(13) and b = F(11)
a = F(19) and b = F(17)
etc.
In general, a = F(6n + 1) and b = F(6n - 1).

Second pattern :
a = F(9) and b = F(7)
a = F(15) and b = F(13)
a = F(21) and b = F(19)
etc.
In general, a = F(6n + 3) and b = F(6n + 1).

EDIT 4:
Perhaps someone adept at Fibonacci identities
can verify those. It seems like a big undertaking.
But with : a³b + ab³ + a³ + ab² - a² - b² + (1 - k)ab + a - 1 = 0,
which can be transformed to :
k = a² + b² + b + 1 + [(a -1)(a² + 1) - b²] / (ab),
it's only necessary to verify that the fractional term is integral.
From there, two formulae for k should follow.
I therefore predict an infinite number of solutions.

EDIT 5:
Following is a list of Fibonacci numbers with the
pattern for each 'a' and 'b' and a list of 'k' values
I've confirmed, up to near the limit of my computer.

F(0) = 0
F(1) = 1
F(2) = 1
F(3) = 2
F(4) = 3
F(5) = 5 ---> b1
F(6) = 8
F(7) = 13 --> a1 and b2
F(8) = 21
F(9) = 34 --> a2
F(10) = 55
F(11) = 89 --> b3
F(12) = 144
F(13) = 233 --> a3 and b4
F(14) = 377
F(15) = 610 --> a4
F(16) = 987
F(17) = 1597 --> b5
F(18) = 2584
F(19) = 4181 --> a5 and b6
F(20) = 6765
F(21) = 10946 --> a6
F(22) = 17711
F(23) = 28657 --> b7
F(24) = 46368
F(25) = 75025 --> a7 and b8
F(26) = 121393
F(27) = 196418 --> a8
F(28) = 317811
F(29) = 514229 --> b9
F(30) = 832040
F(31) = 1346269 --> a9 and b10
F(32) = 2178309
F(33) = 3524578 --> a10

k1 = 231
k2 = 1425
k3 = 62907
k4 = 428217
k5 = 20043711
k6 = 137328513
k7 = 6450199347
k8 = 44209370601
k9 = 2076875723607
k10 = 14235100872177

EDIT 6:
Yippee! I got my proof that the fractional term above is
an integer for both patterns, in one fell swoop, with many
thanks to steiner1745. Reference :

As for nice, simple formulae for 'k', in terms of Phi, I tried.
For example, for the first pattern, I was successful in getting
a very long and tedious formula, that is not pretty enough to
display. A difficult simplification when you see that :

a = [Ø^(12n+2) + 1] / [Ø^(6n+1)√5]
and
b = [Ø^(12n-2) + 1] / [Ø^(6n-1)√5]

If you feel like doing a good job with that, it's all yours.
 Sponsored resultsKangaroo Express - ApplyFound: Hiring Positions Near You. \$10.50 - \$83.75/hr. Apply Online.HiringJobs.WorkGrabber.netWork At Home \$97/hr\$87/hr Part-Time Job Openings. Apply Today, Get Hired Tomorrow!dailyjobcheck.comLocal JobsView Local Jobs on Ask.com. Try our New Search Results!Ask.com/Local JobsA Job (Hiring)100's of Jobs in Your Area: Full Or Part Time - A JobHiring-Jobs.net

# Other Career Questions

 Are statistics and mathematics jobs thinning out in the USA?I'm from California, but I'm currently in Hawaii and some people who teach here are saying that in the USA those jobs are thinning out. They say our leaders are hiding problems, like reasons for the NASA cuts. I know CA is having lots of problems, but I'm not too familiar with what goes on in other states. I looked online and the prospects seem good right now. Will it continue to be this way, or are they really thinning out? 1 answer - Asked By: nessie - 3/12/2011 What jobs can i get if i major in mathematics?I am trying to apply to the business school at my college but if i dont get in i will have to minor in business instead. if i major in mathematics what jobs can i get with that and a minor in accounting? Do these jobs pay well? 2 answers - Asked By: ikn - 1/29/2010 Is it common for a pure mathematics major to get a cryptography job?Hello, I am becoming increasingly interested in pursuing a career in cryptography, however, my current major is pure mathematics. How often do pure mathematics majors obtain jobs involving computer science and applied mathematics and , more specifically, cryptography? 1 answer - Asked By: ttgtgtgtg - 1/2/2012
 Content is not owned or controlled by Monster. Any content concerns should be addressed with Yahoo! Yahoo! Does not evaluate or guarantee the accuracy of any Yahoo! Answers content. Yahoo! Disclaimer.

## Is this normal for an interviewer to do this?

So today I went in for an interview and I was going in for the 2nd interview by the head chief executive. now this is where it got weird, so she asked me about my previous jobs and said how much she liked that product over that product. then she started talking about her daughter? an her divorce ...then how she didn't finish college because she was making more money doing what she did for this company ... then she talked about how her teenage daughter is a handful... I just played it cool thinking she was using some sort of psychology thing to trick me into saying something stupid. the interview ended and she seemed happy an I was escorted to the door... now I'm freaking confused? is this normal behavior for an executive? like it felt like she was going to burst into tears at one point and tell me her life problems... is this normal? was she trying to see how I react or something?

## What do you say when they ask what you want to be paid? ?

Wen you apply at a job and they ask how mch you want as a salary what do you say?

## How do I get a job with Dodgy work history and no experience?

Basically- no degree, although I have tried completing one in the past and stopped because of physical and mental health issues which were overwhelming to deal with along with going to classes full time. I'm not stupid and I am quite articulate. I am 23 and have only worked for about two years retail in high school and stopped working to go to university. I worked a few months in 2010 retail after I dropped out but it was only a seasonal position, and the only reason why I have not been able to constantly work is because of mental health issues. I had also tried going back to community college during my free time since i left university in 2008/9 and I had panic attacks while in community college, which made my anxiety worse from then on. Well recently I met a good doctor and he prescribed me some meds that are stabilizing my moods and I feel the best I've felt in years, and I'm ready to work. Thing is, I don't know how to get a job now since I've spent literally years being depressed and anxious doing nothing. I don't really have anything to put on my resume, and I never finished my AA degree either. All I've done is cashiering and although I do the job well and I get promoted easily when I do these jobs because I'm a hard worker and I try to go above and beyond what they ask of me,which is the attitude I have no matter what kind of work I'm doing as long as I'm getting paid. But I hate cashiering because it's too easy and I want a job that is more interesting. Any suggestions for me on how to get a job that is NOT Retail with the type of background I have right now? I also realize I have to go to college to get certain types of jobs, I am talking about what I can do right here right now.

## Why honesty, hard work and dedication have no place at work?

Recently I have overlooked for a project at work and I am unable to accept it why? I am hard working, dedicated, maintain a very professional decorum, very cordial with my colleagues and bosses, give respect to one and all. Still people who take the p***, argue with managers, gossip mongers have been selected for some very responsible positions at work. I seriously can't get my head around it why, why unprofessional people who have no work ethics being selected over me, whereas I have a track record of excellent performance and never shy away from any work my manager ask me to do? I am at my lowest point and not getting hold of my manager to ask the question why not me, why them who can't even bother? I am feeling like a complete loser, giving years to this place, building my performance, trust and this is how I get rewarded. Why my life is so shit, anything I wish for turns to dust?

## I have applied for over 100 jobs I have gotten no calls for a job interview, what can i do?

As stated in my question I've applied for multiple jobs and gotten no job interview, you name a place I've applied there. I've said i will work ridiculous hours from like 12am to 5am and nothing. I've said I am willing to work weekends public holidays everything and I have gotten nothing back I am so desperate for money it's not funny.

## What to wear to a job interview VS a career fair?

So I have a nice white button up shirt, business skirt and pants, and a suit jacket. I'm applying for a software development job and I'm very short and can look young so I'm trying to look adult, yet professional. I'm also attractive so I'm trying not to look too sexy. For the career fair I'm thinking of wearing just my nice shirt and a skirt with low heels. My reasoning being it's approachable and attractive without going overboard since the career fair hosts are mostly younger male recent grads. I want to be remembered but not intimidating. For my interviews I was thinking pants, suit jacket (power suit). My reasoning being it'll be older execs and HR people (mostly women) so less sexy with the pants but more powerful with the suit jacket. What do you think?!

## What career or jobs can i get after graduating Information Technology?

I am currently a 1st year irregular college student taking I.T. I transferred schools and my majors never got credited. But it's okay because i am slowly getting the logics in programming in Java. This next semester i am taking a System Analysis and Design(SADSIGN) and i am getting nervous because even though i am pretty good at logics, i am not that good at coding. But since it is a case study, we will be on group, we will be four i think. Project manager, Analyst, Documentation, and the programmer. I am asking what jobs i can get after graduating I.T. because what if i graduated I.T. and still not that good at coding, i am hoping that there will be a jobs that will require less programming. Like Database manager or in Multimedia or in charge of Network. So is there jobs that doesn't require hardcore programming skills?

## Which of these careers would I not have a problem getting a job in?

Account Executive Hospitality Manager Sales Representative Editorial Assistant Advertising Manager Hotel Manager Personnel Specialist Writer/Author Association Administrator Presenter Special Events Coordinator Political Aide Promotions Manager Speech Writer Consumer Affairs Specialist Sportscaster Public Information Officer Communications Director Public Relations Specialist Radio/TV Announcer Technical Writer Telemarketing Specialist Customer Service Rep. Fund Raiser Training & Development Specialist Events Planner Flight Attendant Youth Worker Media Manager Recruiter Market Research Analyst Community Action Director Recreation/Attractions Manager Restaurant Manager Campaign Manager Development Director Script Writer Photojournalist Advertising Copywriter Museum Director Greeting Card Writer Production Assistant Actor, Mime Narrator Stage Manager Director Impersonator Make-up Artist Stunt Coordinator Booking Agent Talent Scout Drama Coach Stand-in Playwright Stage Manager Movie Theater Manager

## What jobs can you get from going to an engineering school?

The question explains it, i am thinking of going to an engineering high school but of course it will focus on other stuff too but still. What kind of jobs can you get because i dont want to be a mechanic(no offence to any) but please help me!

## What's the difference between computer science and computer engineering majors?

Can someone tell me te difference between computer science and a computer engineering major. Is it the same?

## How can l find a job in the pharmacitical field as a sales and marketing manager,in south africa?

L want to study medicine and work as a doctor but l am limited due to luck of required monyes. however l swtched on to anther career but still within my career interests as a care giver, but this is somthing to do with sales and marketing in the pharmcitical industry.

## What is the difference between a nurse practitioner and an ARNP?

Is there any difference between a "nurse practitioner" and an "advanced registered nurse practitioner"?

## How could I better prepare myself for a second interview?

My second interview is on Monday and I want to be prepared. It's for an assistant controller position. I've already met with the controller and the hr manager. Monday I will be meeting with the president of the company. How could I prepare myself for Monday's interview? Thanks! Any comments would be great!

## I want to become an Escrow Officer, does anyone know how to go about it? What kind of training will I need?

I know that Escrow is within Title industry in Texas. What would be the best way to get my foot in the door. I am assuming I will have to start as an Escrow assistant and work my way up, but I would really like to find out more about this career path. How does an officer usually get licensed? Are there classes we need to take and exam to take? Any response is appreciated.

## Web designer looking to jump into web producing at large agency. would love your advice!?

I've always freelanced as a web designer and might have an opportunity to work at a large ad agency. sorta nervous about the culture and role, so I was wondering if I could solicit feedback about the type of strengths I might need to develop, ie., strong project management (learn to use basecamp!), etc. I've held jobs on the client side as a web marketing manager and before that freelanced -- but on the very small scale. anyone with similiar experiences or feedback I'd love to hear from you!

## How much do you tip an electrican?

I have to get an electrican to fix an overloaded circuit and possible short. so do you tip and if so, how much?
 Search Career Snapshots Career Benchmarking Career Advice Skills Analysis & Training Questions & Answers SEARCH

## Popular Job Searches

Explore Jobs and Career Opportunities

## Popular Program Searches

Further Your Career With A Degree

## Popular Articles

Browse Articles Related To Careers
2013 Marketing Jobs Outlook
The US may be facing another year of anemic hiring overall, but that won't be the case in the high-orbit world of multichannel, digital media marketing.
2013 Engineering Jobs Outlook
Engineers will find job opportunities in select disciplines in 2013, with candidates who are all-around, client-oriented businesspeople in demand.
Best-Paying Jobs by Major
What could you earn with a particular four-year degree? Find out by checking out this list of the top-paying jobs for 20 of the most common majors.
Eight High-Paying, Secure Jobs
Want to earn a good salary and enjoy a measure of job security as well? Check out these well-paying jobs on tap for fast growth in the coming years.
2013 Finance Jobs Outlook
Three things predict whether your finance job search will fly or flop in 2013: your skills, your industry knowledge and (surprise!) the federal budget.

## Monster Communities

Teaching Community
Where teachers meet and learn.
ArtBistro
Create and connect.
Excelle
Networking for the career-minded woman.
Where nurses call the shots.
More Monster Communities

## Monster Partners

Scholarships
Scholarships, financial aid and more ways to pay for school.
Education.org
Find top campus and online degree programs.
Military.com
Military portal for the US Army, Navy, Air Force, Marine Corps and Coast Guard.
Financial Aid
Scholarships & financial aid.
Staffing for Government Jobs
Staffing and hiring solutions for federal government agency jobs.
More Monster Partners

## Job Hunt Strategy

If you want to blow your chances with recruiters -- and, by extension, with the companies they work for -- here are six perfect ways to do so.

## Resumes & Cover Letters

Hoping to relocate? Get the ball rolling on landing the right job in the right location with these expert resume and cover letter tips.

## Interviewing

Interview questions can run the gamut. You probably won't face all 100 of these, but you should still be prepared to answer at least some of them.

## Salary & Benefits

Most of us aren't natural negotiators, but asking these 10 questions during salary negotiations can help you get everything you deserve.

## Attracting Candidates

Recruiting? Go where the talent is. See why recruiters have befriended social networks.

## Employee Sourcing

November Monster Employment Index Grows 13% Year-Over-Year, Tenth Consecutive Month of Positive Annual Growth.

## Interviewing Candidates

What’s the key to a great interview? According to experts: Practice, practice, practice.

## Workforce Planning

Social media. It’s everywhere. But how can it help you? Learn how to utilize social media even monetize it.

## For Seekers

Campus and Online Degrees
Free Salary Wizard
What are you worth? Find out and negotiate a better salary.
Research Careers
Get information on jobs and career paths to help guide your choices
Resume Distribution Service
Our distribution service puts your resume right in the hands of recruiters.
Resume Writing Services
Our experts will craft a keyword-rich resume that stands out in the crowd.
More Career Resources

## For Employers

Target your job posting to more candidates on thousands of websites.
Hire Right Background Checks
Explore our background check packages to improve the quality of your hires.
Job Postings
Find the right solution for your hiring needs. Starting at \$99.
Power Resume Search
Monster's new search technology precisely matches people with your jobs.
Resource Center
Find staffing insights, labor trends, HR best practices and more.
Target Post
Connect with skilled, hourly and administrative candidates for only \$99.

## Social Media

Find jobs in your area and industry.
Monster Careers
Tune into our career advice and discussions tackling a wide range of topics and industries.
Monster Corporate & PR
Stay up-to-date on the latest news. Get the 'Who', 'What', 'When', and 'Why' on all things Monster related.
Monster Customer Service
Got a Monster question? We've got the answer. Whether you're a job seeker or employer, we can help you find the answers you need.
Monster for Employers
Check out our many pages and stay connected with the latest industry news, events, career advice and job openings.

Tap into Monster's online career forums and share advice with experts.
Monster Company Profiles
Explore companies and get information to guide your career decisions.
Compare Salaries