Consider a function $f$ from the positive rationals to the reals such that $f(x)f(y)\ge f(xy)$ and $f(x+y)\ge f(x)+f(y)$. Further assume this function has a fixed point greater than $1$. Prove this function fixes every point in its domain. (Found this on the IMO website and am sadly unable to solve thus far.)
2026-04-04 15:17:16.1775315836
Fixed Points of Function from Rationals to Reals
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