Sum

Show that every positive odd integer is of the form (4q + 1) or (4q + 3), where q is some integer.

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#### Solution

According to Euclid's division lemma,

a = bq + r where 0 ≤ r ≤ b

Now, let a be an odd positive integer and b = 4.

When 0 ≤ r ≤ 4 so, the possible values of r will be 0, 1, 2, 3.

Now, the possible values of a will be thus, 4q, 4q + 1, 4q+2, 4q +3 where q is an integer.

But, we already know that a is an odd positive integer.

So, a will be 4q + 1 and 4q + 3.

Concept: Euclid’s Division Lemma

Is there an error in this question or solution?

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