P15

Part of 2018 Latvia Baltic Way TST

Problems(1)

Choose n to get 2018 solutions to a system of equations

Source: 2018 Latvia BW TST P15

Determine whether there exists a positive integer

n

such that it is possible to find at least

2018

different quadruples

(x,y,z,t)

of positive integers that simultaneously satisfy equations

\begin{cases} x+y+z=n\\ xyz = 2t^3. \end{cases}

number theorynumber theory unsolvedsystem of equationsalgebra