Strengthening of FLT

Question

FLT is that there are no positive nontrivial integer solutions to the Diophantine equation $a^n + b^n = c^n$ for $n>2$. What about the conjecture that there are no nontrivial solutions to the DE $a^n + b^n = c^n + d^n$ for $n>4$; is there an explicit name for it? I know that it’s a case of Lander, Parkin, Selfridge, but does this particular case have its own name? It’s so natural that it must have its own name, one would figure.