MathDB

1

Part of 2013 Grand Duchy of Lithuania

Problems(1)

f(x) - g(x) is an integer , f(x) is an integer iff g(x) is an integer

Source: 2013 Grand Duchy of Lithuania, Mathematical Contest p1 (Baltic Way TST)

10/3/2020
Let f:R→Rf : R \to R and g:R→Rg : R \to R be strictly increasing linear functions such that f(x)f(x) is an integer if and only if g(x)g(x) is an integer. Prove that f(x)−g(x)f(x) - g(x) is an integer for any x∈Rx \in R.
functionalIncreasingInteger