5^x + 12^y equals 13^z has Unique Solution
Theorem
The Diophantine equation:
- $5^x + 12^y = 13^z$
has exactly one solution in integers:
- $5^2 + 12^2 = 13^2$
Proof
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Sources
- 1993: Nobuhiro Terai: The Diophantine equation $x^2 + q^m = p^n$ (Acta Arithmetica Vol. 63: 351 – 358)
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2$
