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Use Euclid's division lemma to show that...

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.[Hint: Let x be any positive integer then it is of the form `3q`, `3q+1`or `3q+2`Now square each of these and sho

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To show that the square of any positive integer is either of the form \(3m\) or \(3m + 1\) for some integer \(m\), we will use Euclid's division lemma. ### Step-by-step Solution: 1. **Understanding Euclid's Division Lemma**: According to Euclid's division lemma, any integer \(a\) can be expressed in the form: \[ a = 3q + r ...
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