SOLUTION: Prove algebraically that when n squared is divided by 4, the remainder is 1. N is any odd number.

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Question 210775: Prove algebraically that when n squared is divided by 4, the remainder is 1. N is any odd number.
Answer by Alan3354(69443) About Me  (Show Source):
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Prove algebraically that when n squared is divided by 4, the remainder is 1. N is any odd number.
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Any odd number can be represented by
2n+1, where n is any integer.
N = 2n+1
(2n+1)^2 = 4n^2 + 4n + 1
(4n^2 + 4n + 1)/4 = n^2 + n Remainder 1
QED