Explain that odd positive integer to be a perfect square, Mathematics

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Show that for odd positive integer to be a perfect square, it should be of the form

8k +1. Let a=2m+1

Ans: Squaring both sides we get a2 = 4m (m +1) + 1

∴ product of two consecutive numbers is always even

m(m+1)=2k

a2=4(2k)+1 a2 = 8 k + 1

Hence proved

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