3^x + 4^y equals 5^z has Unique Solution/Mistake
Jump to navigation
Jump to search
Source Work
1997: David Wells: Curious and Interesting Numbers (2nd ed.):
- The Dictionary
- $2$
Mistake
- Also, the only solution of $3^x + 4^y = 5^z$ in integers is $x = y = z = 2$. The equation $5^x + 12^y = 13^z$ has the same unique solution.
Correction
What it should say is:
- Also, the only solution of $3^x + 4^y = 5^z$ in (strictly) positive integers is $x = y = z = 2$ ...
as we also have the solutions:
\(\ds 3^0 + 4^1\) | \(=\) | \(\ds 5^1\) | ||||||||||||
\(\ds 5^0 + 12^1\) | \(=\) | \(\ds 13^1\) |
In the original work from which Wells's information was taken, the correct specification for $x$, $y$ and $z$ was used.
This factoid was not included in the first edition of Curious and Interesting Numbers.
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2$