perplexus.info :: Just Math : Find the remainder

Find the remainder (Posted on 2015-01-09)

A. Determine the remainder when 5^(5^5) is divided by 13.
B. Determine the remainder when 9^(9^9) is divided by 41.

See The Solution Submitted by K Sengupta

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Comment 3 of 3 |

Powers of 5 mod13 cycle through 5,-1,-5,1 so 5^5 = 5^1 mod13 and 5^(5^5) = 5.

Powers of 9 mod41 cycle through 9,-1,-9,1 so 9^9 = 9^1 mod 41 and 9^(9^9) = 9.

Posted by xdog on 2015-01-09 10:56:25

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