MathNet 1984 — Part 01 Question 11

Let $a, b, c$ and $d$ be odd integers such as $0\lt a\lt b\lt c\lt d$ and $a d = b c$. Show that if $a + d = 2^{k}$ and $b + c = 2^{m}$ for certain integers $k$ and $m$, then $a = 1$.