On the Diophantine equations x ² − 27y ² = 1 and y ² − 2 ^p z ² = 25

Abstract

In recent years, scholars have paid much attention to the problem of solving the diophantine equations x2 − D1y2 = m, (D1 ∈ Z+, m ∈ Z) and y2 − D2z2 = n, (D2 ∈ Z+, n ∈ Z).