Question 1
Let $a,b,c$ be distinct positive integers such that the product of any two of them plus 1 is a perfect square. Write $ab+1=r^2$, $ac+1=s^2$, $bc+1=t^2$, where $r,s,t$ are positive integers. Suppose $0\lt a\lt b\lt c$. Prove that $\dfrac{rs}{t}$ is not a positive integer.