Question

show that the square of any odd integer is
of the form 49 + 1 for integer q


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Answer 1

Answer:

Then, by Euclid's algorithm, a = 4m + r for some integer m ≥ 0 and r = 0,1,2,3 because 0 ≤ r < 4. Here, a cannot be 4m or 4m + 2, as they are divisible by 2. ... = 4q + 1, where q is some integer. Hence, The square of any odd integer is of the form 4q + 1, for some integer q.

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Answer 2

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