4
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Respected Mathematicians,

The Diophantine equation

$$2^x + 5^y = z^2$$

has solutions $$x = 3, y = 0, z = 3$$ and $$x = 2, y = 1, z = 3$$ I got these solutions by trial and error method. To be honest, these solutions are below the number $5$. So, I easily verified them by trial and error method. I would like to know the method which will give the solutions of the above equation, as well as the solutions of equations below.

a)

$$4^x + 7^y = z^2$$

b)

$$4^x + 11^y = z^2$$

Looking forward to your solution and support. baba

2 Answers 2