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Strange divisibility (Posted on 2005-05-25) Difficulty: 2 of 5
Without evaluation of it, prove that the number N = 27,195^8 - 10,887^8 + 10,152^8 is divisible by 26,460.

Note: the original problem mistakenly listed the last number as 26,640. This has been corrected

See The Solution Submitted by pcbouhid    
Rating: 3.6667 (3 votes)

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strange | Comment 2 of 27 |

I interpret they all are natural numbers.

The first number would finish in 5; the second in 1 and the third in 2. The whole would finish in (5 -1 + 6) = 2. But 26.640 multiples always finishes in 0. So it is not divisible.


  Posted by armando on 2005-05-25 15:29:35
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