Recent content by koukou

thank you i have done this one but still no idea to do this one Prove that n|φ(a^n-1) for every integer a≥2 and any positive integer n

there exists a such that and xs1=y s2x=y..

#1 a) If ex = x for some elements e,x belong to S, we say e is a left identity for x; similarly, if xe = x we say e is a right identity for x. Prove that an element is a left identity for one element of S if and only if it is a left identity for every element of S. Let S be a non-empty set with...

Recall the definition of n! (read n factorial"): n! = (n)(n-1)(n-2) ….(2)(1) =∏(k) In both (a) and (b) below, suppose p≥3 is prime. (a) Prove that if x∈ Zpx is a solution to x square ≡1 (mod p), then x ≡±1 (mod p). (b) Prove that (p-1)!≡±1 (mod p) Zpx x shoud be above p a and b looks...

prove Byron's Conjecture. Define the set Znx={k∈Zn but not including zero ：gcd(k; n) = 1} (a) Prove that Znx is a group under multiplication (mod n). (b) Prove that an element a∈Zn is invertible in Zn (with respect to multiplication (mod n)) if and only if a∈Znx Znx x should be above n . i...