Prove that there is not a positive integer $n$ such that numbers $(n+1)2^n, (n+3)2^{n+2}$ are both perfect squares.
Problem
Source: Greece JBMO TST 2015 p3
Tags: number theory, Perfect Squares, Perfect Square, positive integer
Source: Greece JBMO TST 2015 p3
Tags: number theory, Perfect Squares, Perfect Square, positive integer
Prove that there is not a positive integer $n$ such that numbers $(n+1)2^n, (n+3)2^{n+2}$ are both perfect squares.