Question

show that the square of any odd integer is of the form 4q+1 for some integer q.

Answer 1

What didn't you understand about shubhamsrg's solution?

Answer 2

no

Answer 3

You have an odd number, of the form \(2n+1\). By definition, odd numbers are of this form. Then, \[(2n+1)^2=4n^4+4n+1\]Factor the 4 out, you get\[4(n^2+n)+1\]By definition, this is of the form you want.

What didn't you understand about this?