Question

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

Answer 1

Hey ,

An odd positive integer is of the form 2n+1 for n as a whole number , now ,
(2n+1)² = 4n²+1+4n
= 4n²+4n+1
= 8(n²\2 + n\2)+1
= 8m +1
for m = n²\2 + n\2

wish it helps