Show that any positive odd integer is of the form 6q+1, or 6q+3 , or 6q+5, where q is some integer.

Ans.

Let a be any positive integer and b = 6. Then, by Euclid’s algorithm,
a = 6q + r for some integer q ≥ 0, and r = 0, 1, 2, 3, 4, 5 because 0 ≤
r

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