1. ## Quadratic Residues2

Suppose that n = p1p2 · · · pk is a product of k distinct odd primes. Let a be a
positive integer coprime to n. Show that the congruence x 2a (mod n) is solvable
if and only if each of the congruences x 2a (mod pi) is solvable.

x 2 means x squared

2. Originally Posted by mndi1105
Suppose that n = p1p2 · · · pk is a product of k distinct odd primes. Let a be a
positive integer coprime to n. Show that the congruence x 2a (mod n) is solvable
if and only if each of the congruences x 2a (mod pi) is solvable.

x 2 means x squared
Note $\displaystyle X\equiv a(\bmod b)$ and $\displaystyle X\equiv a(\bmod c)$ if and only if $\displaystyle X\equiv a(\bmod bc)$.