SOLVED

Let $w(n)$ count the number of solutions to
\[n=2^a+3^b+2^c3^d\]
with $a,b,c,d\geq 0$ integers. Is it true that $w(n)$ is bounded by some absolute constant?

A conjecture originally due to Newman.

This is true, and was proved by Evertse, Györy, Stewart, and Tijdeman [EGST88].