If the square of an odd positive integer can be of the form $6 q + 1$ or $6 q + 3$ for some $q$ then q belongs to:

integers

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irrational

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real

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none of these

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Solution

The correct option is A integers
We know that any positive integer can be of the form 6m,6m+1,6m+2,6m+3,6m+4 belongs to integers.

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Show that the square of an odd positive integer can be of the form $6 q + 1$ or $6 q + 3$ for some integer $q$ .

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Show that any positive odd integer of the form 6q+ 1 or 6Q + 3 or 6Q + 5 were q in some integer

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