Consider the expression, get zero remainder (Posted on 2007-05-14)

	Submitted by K Sengupta
Rating: 4.0000 (1 votes)
Solution:	(Hide)
It is readily observed, that the given expression is always even for any positive integer value of n. Now, p^q (mod 5) = p, whenever p = 1,2,3,4 and q = 4t +j, for all j = 1,2,3 and t is a non-negative integer. But p^q = 1 = 1 (Mod 5), whenever p= 1,2,3,4 and q = 4t for any given non-negative integer t, so that: Sum (i=1,2,3,4) (p^q) = 4 (Mod 5), whenever q = 4t for any given non-negative integer t, and: Sum (i=1,..4) (p^q) = (1+2+3+4) (Mod 5) = 0 (Mod 5), whenever q is not equal to 4t. Consequently, it follows that 1^q + 2^q + 3^q + 4^q is always divisible by 10 whenever q is NOT divisible by 4.

	Subject	Author	Date
	another way of getting there	Robby Goetschalckx	2007-05-14 20:00:52
	Solution	Dej Mar	2007-05-14 11:52:46