use euclid's division lemma show that square of any positive integer is either of the form 2n or 2n+1 for the same integer n
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Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m. ∴ square of any positive integer is of the form 3m or 3m+1. Hence proved.
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