TY - JOUR
AU - Biswas, D.
PY - 2022/09/01
Y2 - 2024/02/22
TI - Does the Solution to the Non-linear Diophantine Equation 3x+35y=Z2 Exist?
JF - Journal of Scientific Research
JA - J. Sci. Res.
VL - 14
IS - 3
SE - Section A: Physical and Mathematical Sciences
DO - 10.3329/jsr.v14i3.58535
UR - https://www.banglajol.info/index.php/JSR/article/view/58535
SP - 861-865
AB - <p>This paper investigates the solutions (if any) of the Diophantine equation 3<sup>x</sup> + 35<sup>y</sup> = Z<sup>2</sup>, where , x, y, and z are whole numbers. Diophantine equations are drawing the attention of researchers in diversified fields over the years. These are equations that have more unknowns than a number of equations. Diophantine equations are found in cryptography, chemistry, trigonometry, astronomy, and abstract algebra. The absence of any generalized method by which each Diophantine equation can be solved is a challenge for researchers. In the present communication, it is found with the help of congruence theory and Catalan’s conjecture that the Diophantine equation 3<sup>x</sup> + 35<sup>y</sup> = Z<sup>2 </sup>has only two solutions of (x, y, z) as (1, 0, 2) and (0, 1, 6) in non-negative integers.</p>
ER -