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n is an integer, so 2n+1 is also an integer. 8s+1 is equal to the square of 2n+1, so it's a square number.
2n+1 is an odd integer for any value of n. The square of an odd integer is always an odd integer. Therefore 8s+1=(2n+1)² is odd.
8s+1 is an odd square number.