Solutions of Diophantine Equation x^4 + y^4 = z^2 + 1 for x = 239/Mistake

Source Work

 * The Dictionary
 * $239$
 * $239$

Mistake

 * The 'approximation' to a Fermat equation, $x^4 + y^4 = z^4 + 1$, has $3$ solutions with $x = 239$. The other numbers are $y = 104, z = 58, 136$; $y = 143, z = 60,671$; $y = 208, z = 71, 656$.

Correction
There are $2$ points here:


 * $(1): \quad$ The equation in question is $x^4 + y^4 = z^2 + 1$.


 * $(2): \quad$ It may not necessarily be the case that there are only $3$ solutions. The cited article claims only that these are the only $3$ solutions where $x > y$.