MathDB

4

Part of 2019 Iran RMM TST

Problems(1)

prove lower bound for lcm

Source: Iran RMM TST 2019,day2 p4

7/30/2019
Let a,ba,b be two relatively prime positive integers.Also let m,nm,n be positive integers with n>mn> m .\\ Prove that\\ lcm[am+b,a(m+1)+b,...,an+b]≥(n+1)⋅(nm)lcm [am+b,a (m+1)+b,...,an+b]\ge (n+1)\cdot \binom {n}{m}
Proposed by Navid Safaei
number theoryleast common multiple