Number theory Definition and 475 Threads

Hi I got a question: I have the following problem ax + by = c. Where a,b are positive integers, and c is a known integer. If I calculate the gcd(a,b) is it then possible to find the x,y which makes the above equation true ? Best Regards, Bob

Hey guys, I have a homework assignment for number theory and two of the problems I don't know how do solve. I was hoping I could get some hints or help. Thanks Problem 1 Let m,n be elements of the natural numbers where n > m. and F_n = 2^2^n + 1 a.) Show that (F_n - 2)/F_m is an...

let be the Dirichlet series in the form: g(s)=\sum_{n=0}^{\infty}a(n)n^{-s} my question is if there is a relationship between g(1-s) and g(s) for any L-Dirichlet series. another question...where could i find Vinogradov,s work on Goldbach conjecture?..thanks.

The question is Use Fermat's Theorem to compute the following: 99^{99} \equiv (mod 47) I spent over an hour on it but could only reduce it to 99^7 \equiv (mod 47) I think I am missing something. So if you can help, it would be great. Please provide an explanation as well...

I am doing a course called 'Number Theory'. It is an introductory course to the subject and some if not most of it is based on the book 'Number theory with computer applications' by Ramanjuachary Kumandari and Christina Romero (1998). Anyone have any experince with this book? If so do...

Here you are the best formula to calculate Pi(x) by means of a 4-dimensional integral: \pi(t)=\frac{1}{4\pi^2}\int_0^t\int_{c-i\infty}^{c+i\infty}\int_{d-i\infty}^{d+i\infty}\int_0^{\infty}dxdsdqdn\frac{n^{-s+2}x^{q-1}LnR(qn}}{R(4-s)} Where R(s is the Riemann Zeta function...

I saw someone say this in another thread. Why is it so important? My best guess is that it has something to do with prime factorization, but that's a pretty wild guess.

For all those starting on number theory, here are some notes from the Cambridge first year syllabus. They cover diaphatine equations etc. Regards, M

1. Find seven different unit fractions whose sum is 1. So \frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} + \frac{1}{e} + \frac{1}{f} + \frac{1}{g} = 1 Would this just be purely guess and check? 2. How many different 6 digit numbers can you make using 1,2,5,6,7,9 . Would it just...

Hello all I need help with the following proofs 1. If x and y are arbitrary real numbers, prove that there is at least one real z satisfying x < z < y. (Do I just use the Archimedian Property?) Thanks

Hi, I'm a high school senior in my first semester of Calculus, so my math is pretty limited at the moment. I was wondering if you guys could recommend any introductory number theory books that you think are about at my level. Any suggestions would be really appreciated. Also, sorry if I...

Hello all, here is a problem I am working on that is giving me some problems. p,q, and N are defined as in RSA i.e. {p,q} in (Z_p,*), N = pq a in (Z_n,*) g in (Z_{N^2}) s.t. g=aN+1 mod N^2 The problem is to show that the discrete log problem base g is easy in Z_{N^2}, i.e. : given...

today Alain Connes (with co-author Matilde Marcolli) posted http://arxiv.org/abs/hep-th/0411114 Physics to Number Theory via Non-Commutative Geometry, Part II Part I got a big play on SPR, we should know something about this. Maybe only a little. But something. Part One of "Physics...

Hey, A while ago i hear about finding the division number theory [Tell how a number can be divied be another unmber as a general formula]. And i am wondering if there is a theory "desicovered" the pattern of the prime numbers. Or at least a fixed pattern for predicting some of the prime numbers...

let note f(x)=O(g(x)) this f(x)<MG(x) being M a constant then would it be true?.. If f(n)=o(n^u) then Sum(1<n<x)f(n)=O(n^u+1) adn Int(1,x)dnf(n)=O(n^u+1) Another question let be a(n)n^-s and b(n)n^-s two Dirichlet series so a(n)<b(n) for each n then if b(n)n^-s converges for a number...

Questions: 1) How many zeros are there at the end of 1994! [where n ! stands for n factorial] 2) Prove that if x1, x2, ..., x100 are distinct natural odd numbers 1/x1 + 1/x2 + ... + 1/x100 < 2 3) Prove that if 'p' is a prime number then coefficients of the terms...

Do you know somewhere to download ebooks on Number Theory ? (fundamental and free please :redface:

Hi again, how about the below problem, please give me advice. Let x and y be possitive integers such that 3x+7y is divisible by 11. Which of the following must also be divisible by 11 A. 4x+6y B. x+y=5 C. 9x+4y D .4x-9y E. x+y-1

Can anyone direct me to a good, free, book on basic number theory? Preferably free. :biggrin: But if it isn't, it's not the end of the world. Thanks

Here it is a solution for Pi(x) funciton in number thoeroy using the Laplace transformation and Euler,s transformation for alternating series

Computational Number Theory ?!? I am a student of Computer Science and found many good algorithms on Number Theory while working... But actually...honestly speaking...I don't find good sites on this particular important field...:frown: Or even new works or research... what do you think ?

I want to venture into number theory and I was hoping to get some book recommendation from you guys. Which books do you think best describes and has examples on number theory for a beginner?

I think i have solved the problem of getting the pi(x) function in number theory..i have tried to submit to several webpages but have been rejected so my last resort is to submit to this page hoping that someone give me an oportunity. I am submiting this file from my universty...i have no...

Where I can I find good textbooks on Number Theory?:smile:

do anyone have any website for number theory? if can the whole course of it. i want to start learning it by myself. can anyone introduce a book for me? thank you