On the exponential diophantine equation (n-1)(x) + (n+2)(y) = n(z)

Bai, HairongYuan, Pingzhi2022-12-152022-12-152020-03-30Bai, H. vd. (2020). "On the exponential diophantine equation (n-1)(x) + (n+2)(y) = n(z)". Colloquium Mathematicum, 161(2), 239-249.0010-13541730-6302https://doi.org/10.4064/cm7668-6-2019https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/colloquium-mathematicum/all/161/2/113556/on-the-exponential-diophantine-equation-n-1-x-n-2-y-n-zhttp://hdl.handle.net/11452/29912Suppose that n is a positive integer. We show that the only positive integer solutions (n, x, y, z) of the exponential Diophantine equation (n - 1)(x) + (n + 2)(y) = nz, n >= 2, xyz not equal 0, are (3, 2, 1, 2), (3,1, 2, 3). The main tools in the proofs are Baker's theory and Bilu-Hanrot-Voutier's result on primitive divisors of Lucas numbers.eninfo:eu-repo/semantics/closedAccessExponential Diophantine equationPrimitive divisors of Lucas sequencesJacobi symbolLower bounds for linear forms in two logarithmsPrimitive divisorsLinear-forms2 LogarithmsConjectureNumberLucasMathematicsOn the exponential diophantine equation (n-1)(x) + (n+2)(y) = n(z)Article0005717578000052-s2.0-850847531172392491612MathematicsDiophantine Equation; Number; Linear Forms in Logarithms