Show that for all a co-prime to 561. Hint: 561=3 x 17 x 11.
I thought about trying to show (mod 3,17,11), but do not see how this is possible.
You need just a few elementary facts:
1. If a is co-prime (relatively prime in U.S.) to n and p is any divisor of n, a is relatively prime to p.
2. If a is relatively prime to a prime p,
3. If p, q and r are primes that divide n, then the product pqr divides n.
So by 1 and 2.
Thus 3, 11 and 17 divide and by 3, the product 3*11*17 = 561 divides