By using eculids division lemme show that square of any possitive integer is of the form 3m or 3m+1
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When, r = 0
∴ a = 3q
When, r = 1
∴ a = 3q + 1
When, r = 2
∴ a = 3q + 2
When , a = 3q
On squaring both the sides,
When, a = 3q + 1
On squaring both the sides ,
When, a = 3q + 2
On squaring both the sides,
Therefore , the square of any positive integer is either of the form 3m or 3m+1.
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