System of equations involving a prime
Source: 2022 Bulgarian Spring Math Competition, Problem 10.4
March 27, 2022
algebrasystem of equationsprime
Problem Statement
Find the smallest odd prime , such that there exist coprime positive integers and which satisfy
4k-3\ell=12 \text{ and } \ell^2+\ell k +k^2\equiv 3\text{ }(\text{mod }p)