Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m
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Solution 1
Euclid's Division Lemma states that given any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b.
Let's take a positive integer 'a'. According to Euclid's Division Lemma, we can express 'a' in the form of 3q, 3q+1 or 3q+2 (where q is the quotien Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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