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prove that the square of any …

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prove that the square of any positive integer of the form 5m+1 will have remainder 1 when divided by for some integer m
  • 1 answers

Sia ? 6 years, 4 months ago

Let N = 5q + 1
{tex}\therefore{/tex} N2 = (5q + 1)2
{tex}\Rightarrow{/tex} N= 25q2 + 10q + 1
N2= 5(5q2 + 2q) + 1
= 5m + 1, where q is soqe integer
Hence, the square of any positive integer of the form 5m + 1 will leave a remainder 1 when divided by 5 for some integer m .

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