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  • Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer

Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer

Answers (1)

Any positive integer can be written in the form of 3q or 3q+1 or 3q + 2.
Since square of 3q = 9q² = 3(3q²) = 3m (where 3q² = m)
Square of (3q+1) = (3q+1) ² = 9q²+1+6q = 3(3q²+2q) +1 = 3m + 1
(where, m = 3q² + 2q)
Square of (3q+2) = (3q+2) ² = 9q²+4+12q = 3(3q²+4q) +4 = 3m + 4 (where, m = 3q²+2q)

Thus, there is not any square of a positive integer, which can be written in the form of 3m + 2
Hence the given statement is false.

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infoexpert27

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