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 decided to check my math by evaluating this anyway.
27195^8 = 299166186312683900806365263000390625
10887^8 = 197363020619290527021005277168321
10152^8 = 112826956359514752722139774713856
N= 299081650248424125032066397497936160
N/37= 8083287844552003379245037770214490.810810810810810...
I didn't check the other factors of 26640 but they must have worked themselves out just fine as the repeating decimal is
810/999 = 30/37
30 was the remainder I predicted mod 37 but there was no guarantee that 2^4, 3^2, and 5 were going to leave no remainder.

Posted by Jer
on 20050525 17:47:00 