Mar 21, 2010 · Suppose q is a prime and p=4q+1 is a prime. Prove that 2 is a primitive root modulo p.

Dec 11, 2007 · i have 2 problem and need ur help let r be a primitive root of the integer n . prove that r^k is a primitive root of n if and only if gcd (k,phi (n))=1 Let n>2 be a positive integer. Say …

Nov 19, 2013 · By a primitive 4th root of unity, I assume you mean a y such that y 4 is 1 mod p, but no smaller power is 1. Now if you know about cyclic groups, your problem is easy. …

Jun 8, 2008 · How to find all primitive roots modulo 11^2? I can find some of its primitive roots (e.g: 2), can we find the others by using the found ones?

May 6, 2008 · Let r be a primitive root of the odd prime p . Prove the following. If p is congruent to 3(mod 4), then -r has order (p-1)/2 modulo p.

Jul 8, 2011 · Show that if m is a number having primitive roots, then the product of the positive integers less than or equal to m and relatively prime to m is congruent to -1 (\\mod{m}). m has …

Apr 24, 2010 · Here p denotes a prime. Suppose q is a prime such that q=4n+1 where n is an interger. proof that 2 is a primitive root of p if p is of the form 2q+1. (sophie germain prime).

Oct 15, 2008 · Find a primitive root modulo 89 and use the answer to find a number a so that the order of a modulo 89 is 8. Does this mean a^8=1 (mod 89)?

Nov 16, 2010 · Hi, I have 3 problems concerning primitive roots that I have been unable to work through. Any advice on how to solve these would be greatly appreciated! 1. Show if g, h are …

Aug 22, 2008 · Show that if g is a primitive root of n, then the numbers g, g 2, g 3,, g ϕ (n) form a reduced residue system (mod n) Just show that no two are congruent to eachother. Then by …