How can I transform the following equation:
$$2^y = 615+x^2$$
to something of the form
$$y = \cdots$$
SideQuest:
What would the values of $x$ and $y$ that make the equality True, and how would you get them?
Thanks!
$\endgroup$ 51 Answer
$\begingroup$For sidequest : hint
Assuming that you want a positive integer solution in $x,y$.
$2^y$ can not be congruent to $0$ mod 3.
$x^2$ can not be congruent to $2$ mod 3.
$615$ congruent to $0$ mod 3.
Therefore, $2^y$ and $x^2$ must both be congruent to $1$ mod 3.
Therefore, $y$ must be an even.
This greatly reduces the problem, because now,
$2^y - x^2$ can be readily factored.
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