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Prove that the square of any positive integer is of form 5m,5m+1,5m+4 for some integer m

Answer» Let a be positive integerLet b be 5 and if b is 5 then remainder will be less than 5 Euclid division lemma a+= bq + rSo5m. 5× 1 + 0 = 55m + 1 = 5 × 1 + 1 = 65m + 2 = 5 × 2 + 2= 125m + 3 = 5 × 3 + 3 = 185m + 4= 5 × 4 + 4 = 24#hence proved#
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