Question

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

Answer 1

Heya!!

##Let ‘a’ be given positive odd integer.
If we divide ‘a’ by 4 then by Euclid’s DA
a = 4q + r where 0_< r<4
So r may be 0, 1, 2, 3

putting 1 in place of r

a=4q+1
a^2= (4q+1)^2

a^2=16q^2+8q+1

a^2=8q(q+1) + 1

a^2= 8m+1 where 'm' is equal to q(q+1)

hence square of a positive odd integer is of form 8m +1 for some integer 'm'………………


Hope this helps you ☺☺