Question

How many positive integer solutions are there to the following? This is from a non-calculator test.

Answer 1

Infinitely many.

Explanation:

We have

`color(blue)(2)^2+(2×color(blue)(4)^2)=(4×color(blue)(3)^2)`

And we can just multiply these `x,y,z` values given in blue by a common factor of 2, or 3, or 4, ... .