MathDB
find real so that no square of an integer exists in sequence

Source: Czech-Polish-Slovak Match 2017 day 1 P1

September 28, 2017
Perfect Squaresnumber theorypositive integers

Problem Statement

Find all positive real numbers cc such that there are in finitely many pairs of positive integers (n,m)(n,m) satisfying the following conditions: n≥m+cm−1+1n \ge m+c\sqrt{m - 1}+1 and among numbers n.n+1,....2n−mn. n+1,.... 2n-m there is no square of an integer.
(Slovakia)
Back to ProblemsView on AoPS