VTMO 2015 — Grade 9 — final Question 3

Let $0 \lt a \lt b \lt c$ be integers with $ab + 1 = r^{2} , ac + 1 = s^{2} , bc + 1 = t^{2}$ for positive integers $r , s , t$. Prove $\frac{rs}{t}$ is not an integer.