Question

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

Show that any positive odd integer is of the form 6q + 1 or 6q + 3 or 6q + 5; where q is some integer. Answer: According to Euclid's Division Lemma if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r < b.