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 20050602 20:50:49 