SOLUTION: Prove that (2n+1)^2 - (2n-1)^2 is a multiple of 8 for all positive integer values of n.

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Question 1185342: Prove that (2n+1)^2 - (2n-1)^2 is a multiple of 8 for all positive integer values of n.
Answer by ikleyn(52794) About Me  (Show Source):
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Prove that (2n+1)^2 - (2n-1)^2 is a multiple of 8 for all positive integer values of n.
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    (2n+1)^2 - (2n-1)^2 = (4n^2 + 4n + 1) - (4n^2 - 4n + 1) = 8n,  which is a MULTIPLE of 8 for any integer n.

Proved, solved and explained.

And completed.