Question

show that the square of an odd positive integer is of the form 8m+1 where m is some whole number​

Answer 1

Answer:

We apply Euclid's division algorithm ie. a=bq+r

0<r<8 where r=0,1,2,3,4,5,6,7

a=8q+0

a=8q

by squaring both sides

a²=64q

a²=8(8q) where 8q is m

a²=8m

similarly

a=8q+1

a²=(8q+1)²

a²=64q²+1+16

a²=8(8q+2)+1

a²=8m+1

hence proved,

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