<s>[INST] Show that $2^a|(x-1)$ iff $2^a|(y-1)$. Suppose that $2^n + 1 =xy$, where $x$ and $y$ are integers > $1$ and $n>0$.
Show that $2^a|(x-1)$ iff $2^a|(y-1)$.
Here $a|b$ implies $a$ divides $b$.
 [/INST] $$(x-1)(y-1) = 1 + xy - x - y = 2^n - (x - 1) - (y - 1)$$
Then if $2^a$ divides $(x-1)$ then it definetile divides $(y-1)$, because
$$(y - 1) = 2^n - (x - 1) - (x-1)(y-1).$$
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