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

I suspect, though I'm too lazy to fully delve into it right now, that if you list all the prime factors of each of the three numbers provided (27195, 10887, 10152) repeated 8 times, then do the subtraction and addition on those listed prime factors to come up with a new list of prime factors, you will get a product of 26460.

Is this what you were looking for pcbouhid?

Posted by Erik O. on 2005-06-02 20:50:49