On The Solutions of The Equation (4ⁿ)^x+p^y=z²

2012/02/10 by Peker, Bilge, Cenberci, Selin Inag
#11D61 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1202.2267

Abstract

In this paper, we gave solutions of the Diophantine equations 16^x+p^y=z², 64^x+p^y=z² where p is an odd prime, n is a positive integer and x,y,z are non-negative integers. Finally we gave a generalization of the Diophantine equation (4ⁿ)^x+p^y=z².

Related

• On the Diophantine Equation p^x + p^y = z²ⁿ
• On the solutions of the Diophantine equation (x-d)²+x²+(x+d)²=yⁿ for d a prime power
• Solution of the Diophantine equation x² + p^k=yⁿ
• On the Diophantine equation dx²+p^2aq^2b=4y^p
• A solution to a problem and the Diophantine equation X²+bX+c=Y²