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A 2011 Problem (Posted on 2007-03-17) Difficulty: 3 of 5
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?

See The Solution Submitted by K Sengupta    
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Solution solution Comment 3 of 3 |
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
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