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When n is a odd integer than show that n square-1 is divided by 8

Posted by Sid Siddharth 7 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Unnati Pragya 7 years, 7 months ago

We know that 4q + 1,4q+3 odd positive integer If n=4q+1 n^2-1= 16q^2+8+1-1 n^2-1=8(2q^2+1) n^2-1 is divisible by 8 If n=4q+3 n^2-1=16q^2+24q+9-1 n^2-1= 8(2q^2+3q+1) n^2-1 is divisible by 8 Hence,n^2 -1 is divisible by 8

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CBSE > Class 10 > Mathematics