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## S02 Three ways to reach a Diophantine equation

02. PEN H15 (Balkan Mathematical Olympiad 1998) Prove that there are no integers $x$ and $y$ satisfying $x^{2} = y^{5} -4$.

Here is the official solution file: PEN02S
You can also disscuss the problems here!

Acknowledgement. We would like to express our gratitude to Andrei Frimu who proofreaded the manuscript.