MathDB
Fractional part

Source: Iranian TST 2020, second exam day 2, problem 5

March 12, 2020
fractional partalgebraDivisibility

Problem Statement

For every positive integer k>1k>1 prove that there exist a real number xx so that for every positive integer n<1398n<1398: {xn}<{xn−1}⟺k∣n.\left\{x^n\right\}<\left\{x^{n-1}\right\} \Longleftrightarrow k\mid n.
Proposed by Mohammad Amin Sharifi
Back to ProblemsView on AoPS