I think I improved an Erdős problem how can I verify it?

I’ve been working on an Erdős problem (Problem #961) and believe I’ve made a nontrivial improvement on the known result, specifically, I think I’ve reduced the bound from exponential to polynomial.

I’m relatively new to formal mathematics, so I’m unsure how to properly verify or validate my work.

What are the best steps to take in this situation?

* How can I check whether my result is already known? * Where can I get feedback? * At what point is something worth writing up formally or submitting?

Any guidance would be really helpful.