Solutions of the Diophantine equation nx + (7p)y = z2
Key Points
Integer solutions for nx + (7p)y = z² exist under specific conditions concerning primes.
The exploration focuses on positive n and prime p, with x, y, and z taking non-negative values.
Systematic checks evaluate possible integer combinations to confirm valid outcomes.
This work highlights the need for thorough exploration of integer solution criteria.
Abstract
Our purpose of this paper is to find integer solutions n, p, x, y and z for the Diophantine equation nx + (7p)y = z2 where n is positive, p is prime and x, y . z are non-negative.