Let $a,b $ be two relatively prime positive integers.Also let $m,n $ be positive integers with $n> m $. Prove that $lcm [am+b,a (m+1)+b,...,an+b]\ge (n+1)\cdot \binom {n}{m}$ Proposed by Navid Safaei
Source: Iran RMM TST 2019,day2 p4
Tags: number theory, least common multiple
Let $a,b $ be two relatively prime positive integers.Also let $m,n $ be positive integers with $n> m $. Prove that $lcm [am+b,a (m+1)+b,...,an+b]\ge (n+1)\cdot \binom {n}{m}$ Proposed by Navid Safaei