For all polynomial equations with integer coefficients and related unknowns assumed to be rational integers at this time, we employ the Diophantine equation. This concept is frequently expanded to include any kind of equation involving numbers and having integer unknowns. Fermat's equation xn + bn= cn, where x, b, c, and n > 3 are unidentified positive integers, serves as an illustrative example. When one or more exponents are unknown, the phrase "exponential Diophantine equation" is frequently used. Consider now that here, where min c > 1, b and c are positive integers with fixed coprime. Every positive number solution (x, y, and z) to the equation 3x + by = cz is categorised in this portion of the research paper.
Additionally, we must demonstrate that, if c = b+ 3, the
equation has only positive integer solutions, i.e. (x, y, z) = (3, 2, 2), with
the exception of (b, x, y, z) = (3, 3, 2, 2) and (3r -1, r +3, 3, 3), where r
is a positive integer number of r >= 3.
Author(s) Details:
S. P. Behera,
Department of
Mathematics, C.V. Raman Global University, Bhubaneswar, Odisha, India.
Please see the link here: https://stm.bookpi.org/NRAMCS-V6/article/view/7760
No comments:
Post a Comment