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2016 CNMO Grade 10 P3

Source: 2016 China Northern MO Grade 10, Problem 3

February 24, 2020
number theory

Problem Statement

Prove: (a) There are infinitely many positive intengers nn, satisfying: gcd⁡(n,[2n])=1.\gcd(n,[\sqrt2n])=1. (b) There are infinitely many positive intengers nn, satisfying: gcd⁡(n,[2n])>1.\gcd(n,[\sqrt2n])>1.
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