If \(m\) is a positive integer then the values of \(k\) for which \(6m + k\) cannot be a perfect square are
Question and options
If is a positive integer then the values of for which cannot be a perfect square are
- 3 and 4
- 1 and 5
- 2 and 5
- 1, 2 and 5
Answer and explanation
Correct answer: C - 2 and 5
Perfect squares mod 6 are only 0, 1, 3, 4. So 6m + k is never a square when k is congruent to 2 or 5 mod 6; k = 1 or 4 or 3 can give squares (e.g. 25, 16, 9).
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