- #1
.d9n.
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Homework Statement
Find all solutions in non-negative integers x, y, z of the equation
2^x + 3^y= z^2
Homework Equations
The Attempt at a Solution
not entirely sure how to go about it, I am assuming maybe logarithms?
2=log(base Z) (2^x+3^y)
or maybe substitution
let
u=2^x so x=log(base 2)(u)
v=3^y so y=log(base 3)(v)
w=z^2 so 2=log(base z)(w)
u+v=w → 2^(log(base 2)(u))+3^(log(base 3)(v))=2^(log(base z)(w))