DE-MO 2008 Problem 4

Find the smallest constant $C$ such that for all real $x,y$ $1+(x+y)^2 \leq C \cdot (1+x^2) \cdot (1+y^2)$ holds.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.