Putnam 1959 A3

Find all complex-valued functions $f$ of a complex variable such that $f(z)+zf(1-z)=1+z$ for all $z\in \mathbb{C}$ .

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.