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A 2011 Problem (
Posted on 20070317
)
Determine the remainder when (2011
^{56}
+ 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
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 20070317 14:37:35
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