Register to reply

Finding primes given a condition

by galois427
Tags: condition, primes
Share this thread:
galois427
#1
Oct8-04, 10:52 PM
P: 16
Hi, I need help solving this problem. The question asks me to find all prime numbers p such that p^2 = n^3 + 1 for some integer n.
Phys.Org News Partner Science news on Phys.org
Physicists discuss quantum pigeonhole principle
Giant crater in Russia's far north sparks mystery
NASA Mars spacecraft prepare for close comet flyby
Zurtex
#2
Oct9-04, 07:14 AM
Sci Advisor
HW Helper
P: 1,123
This is really quite easy as p^2 can only be p times p or 1 times p^2.

Now, [tex]n^3 + 1 = (n + 1)(n^2 - n + 1)[/tex]

So one possible solution is where one of the factors is equal to 1 and the other is equal to p^2. Or when they are both equal to each other. Test those out and you should find all the possible solutions for n.
TenaliRaman
#3
Oct13-04, 03:48 PM
P: 646
An alternative,
all odd p^2 is usually of the form
p^2 = 1 mod 4

n^3+1 = 1 mod 4
or n^3 = 0 mod 4

Now this is useful if and only if u have a list of primes ...
So first u can generate a list and then check for conditions ...

-- AI


Register to reply

Related Discussions
Finding small primes (fast determanistic tests) Linear & Abstract Algebra 11
Finding C with inital condition, its wrong, any ideas why? Calculus & Beyond Homework 2
Prime proofs Calculus & Beyond Homework 3
The way of finding primes Linear & Abstract Algebra 10
Prove that the sum of two odd primes will never result in a prime? General Math 3