The Wikipedia article on Sidon sets mentions

Erdős conjectured that there exists a nonconstant integer-coefficient polynomial whose values at the natural numbers form a Sidon sequence. Specifically, he asked if the set of fifth powers is a Sidon set. Ruzsa came close to this by showing that there is a real number $c$ with $0<c<1$ such that the range of the function $$f(x)=x^5+\left\lfloor cx^4\right\rfloor$$ is a Sidon sequence.

I want to know how much (if any) progress have been made on any of the two conjectures of Erdős. In particular, how far has the computers checked the second conjecture?