Write whether every positive integer

Question:

Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.

Solution:

No, by Euclid’s Lemma, b = aq + r,0<,r

i.e., r = 0,1,2, 3 So, this must be in the form Aq, 4q + 1, Aq + 2 or 4q + 3.

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