Question

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

Answer 1

from Euclid division algorithm,any positive integer is represented as
n= q x m + r
for odd integer
$n = 2 \times m + 1 \\ {n}^{2} =( {2m + 1)}^{2} \\ {n}^{2} = 4 {m}^{2} + 1 + 4m$
either this is incomplete question,because with given data this can solve that much only.