Details

Autor(en) / Beteiligte

• Izadi, Farzali
• Baghalaghdam, Mehdi

Titel

On the simultaneous Diophantine equations m·(x1k+x2k+⋯+xt1k)=n·(y1k+y2k+⋯yt2k); k=1,3

Ist Teil von

• Periodica mathematica Hungarica, 2017, Vol.75 (2), p.190-195

Ort / Verlag

Dordrecht: Springer Netherlands

Erscheinungsjahr

2017

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, we solve the simultaneous Diophantine equations m · ( x 1 k + x 2 k + ⋯ + x t 1 k ) = n · ( y 1 k + y 2 k + ⋯ + y t 2 k ) , k = 1 , 3 , where t 1 , t 2 ≥ 3 , and m , n are fixed arbitrary and relatively prime positive integers. This is done by choosing two appropriate trivial parametric solutions and obtaining infinitely many nontrivial parametric solutions. Also we work out some examples, in particular the Diophantine systems of A k + B k + C k = D k + E k , k = 1 , 3 .