MathDB
Gcd of binomial coefficient and integer is 1

Source: China Second Round 2009

February 18, 2012
number theorygreatest common divisornumber theory proposed

Problem Statement

Let k,lk,l be two given integers. Prove that there exist infinite many integers m≥km\ge k such that gcd⁡((mk),l)=1\gcd\left(\binom{m}{k},l\right)=1.
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