On the Diophantine Equation 5 x + p mn y = z 2 - Bakar, H. S.; Sapar, S. H.; Johari, M. A. M. (Institute for Mathematical Research, Universiti Putra Malaysia, 2019)
Diophantine equation is a polynomial equation with two or more unknowns for which only integral solutions are sought. This paper concentrates on finding the integral solutions to the Diophantine equation 5 x + p mn y = z 2 where p > 5 a prime number and y = 1, 2. The positive integral solutions to the equation are (x, m, n, y, z) = (2r, t, pt k 2 ± 2k5 r , 1, pt k ± 5 r ) and 2r, 2t, 5 2r−α − 5 α 2p t , 2, 5 2r−α + 5α 2 for k, r, t ∈ N where 0 ≤ α < r.