SOLUTION: can you please show me how to solve the following problem: show that the statement is true for n^2-n+2 is divisible by 2

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Question 438234: can you please show me how to solve the following problem: show that the statement is true for n^2-n+2 is divisible by 2
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
n%5E2+-+n+%2B+2
Let n be any even integer. ==> n = 2k ==>n%5E2+-+n+%2B+2+=+4k%5E2+-+2k+%2B+2+=+%0D%0A%0D%0A2%282k%5E2+-+k+%2B+1%29, hence the expression is even.
Let n be odd. ==> n = 2k-1 ==> , and so again the expression is even.