Question

Let m and n be two positive integers.
Show that (36 m+ n)(m+36 n) cannot be a power of 2.

Answer 1

what do you get when you multiply them?

Answer 2

\[ \large (36m+n)(m+36)=36(m+n)^2+5^23^27mn=9[4(m+n)^2+5^27mn] \]
hence it cannot be a power of 2