MathDB

3

Part of 2018 Bulgaria JBMO TST

Problems(2)

n^6 + 5n^3 + 4n + 116 is the product of two or more consecutive numbers

Source: Bulgaria JBMO TST 2018, Day 1, Problem 3

6/25/2018
Find all positive integers nn such that the number n6+5n3+4n+116n^6 + 5n^3 + 4n + 116 is the product of two or more consecutive numbers.
number theoryDiophantine equation
Weird inequality from Bulgaria JBMO TST 2017

Source: Bulgaria JBMO TST 2017, Day 2, Problem 3

6/25/2018
Prove for all positive real numbers m,n,p,qm,n,p,q that mt+n+p+q+nt+p+q+m+pt+q+m+n+qt+m+n+p≥45,\frac{m}{t+n+p+q} + \frac{n}{t+p+q+m} + \frac{p}{t+q+m+n} + \frac{q}{t+m+n+p} \geq \frac{4}{5}, where t=m+n+p+q2.t=\frac{m+n+p+q}{2}.
inequalities