Question

# Use Euclid's division lemma to show that the square of any positive integer is either of the form or for some integer m, but not of the form .

Hard
Solution
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## Let be the positive integer and .We know , Now, , The possibilities of remainder is or .Case 1 : When  where Case 2 : When  where Case 3: When  where Hence, from all the above cases, it is clear that square of any positive integer is of the form or .

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