Question

Show that the Square of any positive integer cannot be of the form 6m+2 or 6m+5 for any Integer m.

Answer 1

Lets assume the value of integer m to be 5.

6(5) + 2 = 32

6(5) + 5 = 35

This clearly shows that both forms are incorrect as $5^{2} = 25$

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Answer 2

Here is the answer......

It can be done by the

Euclid's division lemma.

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