Open AccessOn exponential Diophantine equation 17x+83y= z2and 29x+71y= z2
Author(s) -
Komon Paisal,
Pailin Chayapham
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2070/1/012015
Subject(s) - diophantine equation , physics , integer (computer science) , combinatorics , mathematics , programming language , computer science
This Diophantine is an equation that many researchers are interested in and studied in many form such 3 x +5 y · 7 z = u 2 , (x+1) k + (x+2) k + … + (2x) k = y n and ka x + lb y = c z . The extensively studied form is a x + b y = c z . In this paper we show that the Diophantine equations 17 x +83 y = z 2 and 29 x +71 y = z 2 has a unique non – negative integer solution (x, y, z) = (1,1,10)