SOLUTION: Prove that if n is any integer not divisible by 5, then n has a square that is either of the form 5k+1 or 5k+4, where k is some integer.

Question 755184: Prove that if n is any integer not divisible by 5, then n has a square that is either of the form 5k+1 or 5k+4, where k is some integer.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If n is any integer not divisible by 5, when we divide it by 5 we get 1, 2, 3, or 4 as a remainder. That means that
(remainder=1), or
(remainder=2), or
(remainder=3), or
(remainder=4),
for some integer p.

If , then
,
which is with
If , then
,
which is with
If , then
,
which is with
If , then
,
which is with
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