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
27195 and 26640 are 0 mod 37
10887 is 9 mod 37
10152 is 14 mod 37
9^8 = ((9^2)^2)^2 = (7^2)^2 = 12^2 = 33 mod 37
14^8 = ((14^2)^2)^2 = (11^2)^2 = 10^2 = 26 mod 37
0  33 + 26 = 7 = 30 mod 37 so N is not divisible by 26640

Posted by Jer
on 20050525 17:30:49 