TUYMAADA 2017 S5

Does there exist a quadratic trinomial $f(x)$ such that $f(1/2017)=1/2018$ , $f(1/2018)=1/2017$ , and two of its coefficients are integers?

(A. Khrabrov)

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.