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China Team Selection Test 2017 TST 2 Day 2 Q4

Source: China Shanghai ,Mar 12, 2017

March 12, 2017
number theoryalgebraChina TST

Problem Statement

An integer n>1n>1 is given . Find the smallest positive number mm satisfying the following conditions： for any set {a,b}\{a,b\} ⊂{1,2,⋯ ,2n−1}\subset \{1,2,\cdots,2n-1\} ,there are non-negative integers x,y x, y ( not all zero) such that 2n∣ax+by2n|ax+by and x+y≤m.x+y\leq m.
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