Let $ a $, $ b $, $ c $ be fixed coprime positive integers with $\min\{a, b, c\}> 1$. In this
survey, we consider some unsolved problems and related works concerning the positive …

On the exponential Diophantine equation (3m2 + 1)x + (qm2 − 1)y = (rm)z Page 1 SUT Journal
of Mathematics Vol. 56, No. 2 (2020), 147–158 On the exponential Diophantine equation (3m2 …

Abstract Let (a, b, c) be a primitive Pythagorean triple with 2∣ b. Then, we have a= m 2-n 2,
b= 2 mn, c= m 2+ n 2, where m, n are positive integers such that m> n, gcd (m, n)= 1 and m≢ …

On the Exponential Diophantine Equation $$(m^2+m+1)^x+m^y=(m+1)^z $$ | Mediterranean
Journal of Mathematics Skip to main content SpringerLink Account Menu Find a journal Publish …

Abstract Let (m,\n)(m, n) be fixed positive integers such that m> n,\gcd (m,\n)= 1 m> n, gcd
(m, n)= 1 and mn ≡ 0\pmod 2 mn≡ 0 (mod 2). Then the triple (m^ 2-n^ 2,\2mn,\m^ 2+ n …

On the exponential Diophantine equation mx + (m + 1) y = (1 + m + m Page 1 DOI: 10.2478/auom-2021-0032
An. St. Univ. Ovidius Constanta Vol. 29(3),2021, 23–32 On the exponential Diophantine …

Abstract Let (a, b, c) be a primitive Pythagorean triple satisfying a 2+ b 2= c 2. In 1956,
Jeśmanowicz conjectured that the exponential Diophantine equation (na) x+(nb) y=(nc) z …

Abstract Let (a, b, c) be a primitive Pythagorean triple. Set a= m^ 2-n^ 2 a= m 2-n 2, b= 2mn
b= 2 mn, and c= m^ 2+ n^ 2 c= m 2+ n 2 with m and n positive coprime integers, m> nm> n …