Given positive integers a and b such that $a\mid b^2, \:b^2\mid a^3, \:a^3\mid b^4,\: b^4\mid a^5$..., prove $a=b.$
Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?