Determine the remainder when (2011⁵⁶ + 34)²⁸ is divided by 111.

Can you do this in a short time using pen and paper, and eventually a hand calculator, but no computer programs?

2011 mod 111 = 13
56=8 * 7
13^8 = 815730721 = 46 mod 111
46^7 = 435817657216 = 16 mod 111
16 + 34 = 50
28=4 * 7
50^4 = 6250000 = 34 mod 111
34^7 = 52523350144 = 70 mod 111, which is the answer

Posted by Charlie on 2007-03-17 14:37:35