Question

Show that any +ve even integers is of the form 6q, 6q+2, 6q+4 where q is some integer using Euclid's division lemma.
$a = bq + r$
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Answer 1

ANSWER♡

Let ‘a’ be any positive even integer and ‘b = 6’.Therefore, a = 6q +r, where 0 ≤ r < 6.Now, by placing r = 0, we get, a = 6q + 0 = 6qBy placing r = 1, we get, a = 6q +1By placing, r = 2, we get, a = 6q + 2By placing, r = 3, we get, a = 6q + 3By placing, r = 4, we get, a = 6q + 4By placing, r = 5, we get, a = 6q +5Thus, a = 6q or, 6q +1 or, 6q + 2 or, 6q + 3 or, 6q + 4 or, 6q +5.But here, 6q +1, 6q + 3, 6q +5 are the odd integers.Therefore, 6q or, 6q + 2 or, 6q + 4 are the forms of any positive even integers.

Answer 2

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