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Real Numbers

Use Euclid's ...

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Use Euclid's division lemma to show that the square of any positive integers is either of the form 3m or 3m+1 for some integer m

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Q. Question 4
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 show that they can be rewritten in the form 3m or 3m + 1.]

What is the reason behind taking b =3 in Question:

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. [4 MARKS]

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