Is the polynomial
$$P_n(x,y)=\displaystyle\sum_{a+b\leq n}x^ay^b$$
irreducible in $\mathbb Z[x,y]$?
For all $n\leq 500$ this is true (checked using Mathematica), so it is reasonable to presume that it is true for all $n$.
This question is related to another problem posted on this forum. Namely,
$$P_n(x,1)=\sum_{0\leq i\leq n} (n-i+1)x^i=f_n(x)$$
so it is easy to see that proving that $f_n(x)$ is irreducible should be enough. But this seems to be open...
