If n is even then (n-1)^2 is odd or even??
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N is even...therefore,(n-1) will be odd
And square of any odd number is odd....so (n-1)^2 is odd
And square of any odd number is odd....so (n-1)^2 is odd
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If n is even, then there are integer k such n=2k
If n is even, then n -1=2k-1 is odd.
(n - 1)² = (2k-1)² = 4k² -4k +1 = 4(k² - k) + 1 = 2(2k² -2k) + 1 = 2q + 1
So if n is even, then (n-1)² is odd.
For example:
6 is even
(6 - 1)² = 5² = 25 (is odd)
If n is even, then n -1=2k-1 is odd.
(n - 1)² = (2k-1)² = 4k² -4k +1 = 4(k² - k) + 1 = 2(2k² -2k) + 1 = 2q + 1
So if n is even, then (n-1)² is odd.
For example:
6 is even
(6 - 1)² = 5² = 25 (is odd)
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