This study aims to identify all integer solutions for specific Diophantine equations.
Utilized Matveev theorem for proof.
Employed Dujella-Pethő reduction lemma for analysis.
Identified conditions for integer solutions (k, m, n) in the equations.
Resumen
This study aims to find all possible solutions (k, m, n) of the Diophantine equations Pₖ=Rₘ Rₙ and Rₖ=Pₘ Pₙ. Our proof is conducted with the famous Matveev theorem and Dujella-Pethő reduction lemma.