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Show that p square will leave a remainder 1 when divided by 8 if P is an odd positive integer

Posted by Chanchal Tanwer 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 7 months ago

P = 2n + 1 where n = 0, 1, 2, 3, 4, ...
=> p² = 4n² + 4n + 1
= 4(n² + n) + 1
= 4n(n+1) + 1
but n(n+1) is even because if n is odd, n+1 is even - otherwise n is even
therefore 4n(n+1) + 1 = 8m + 1 where m is an integer.
=> p² = 1

1Thank You

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