Tamref's Last Theorem/Mistake

Source Work

1986: David Wells: Curious and Interesting Numbers:

The Dictionary

$2$

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary

$2$

Mistake

Fermat's equation being exceedingly difficult to solve, several mathematicians have noticed in an idle moment that $n^x + n^y = n^z$ is much easier. Its only solutions in integers are when $n = 2$, and $2^1 + 2^1 = 2^2$.

Correction

In fact $2^x + 2^y = 2^z$ has solutions for all $x \in \Z$, whence $y = x$ and $z = x + 1$, for example:

\(\ds 2^2 + 2^2\)

\(=\)

\(\ds 2^3\)

\(\ds 2^{-4} + 2^{-4}\)

\(=\)

\(\ds 2^{-3}\)

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2$