A linear Diophantine equation equates the sum of two or more unknowns, with coefficients, to a constant. An exponential Diophantine equation is one in which unknowns can appear in …

A Diophantine equation is an equation relating integer (or sometimes natural number or whole number) quanitites. Finding the solution or solutions to a Diophantine equation is closely tied …

Diophantine equation, equation involving only sums, products, and powers in which all the constants are integers and the only solutions of interest are integers. For example, 3 x + 7 y = …

Dec 3, 2025 · A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary …

Just the integers, please. Can we solve an equation like this using only integers? ax + by = c. It is Linear because the variables x and y have...

The most famous diophantine equation is the Fermat equation xd + yd zd = 0. For d = 2 there are many integer solutions, and for d 3 there are no positive integer solutions.

Aug 18, 2022 · The study of Diophantine equations is on the border-line between number theory and algebraic geometry (cf. Diophantine geometry). Finding solutions of equations in integers …

A Diophantine equation is a polynomial equation with 2 or more integer unknowns. A Linear Diophantine equation (LDE) is an equation with 2 or more integer unknowns and the integer …

A diophantine equation is an algebraic equation, or system of equations, in several unknowns and with integer (or rational) coefficients, which one seeks to solve in integers (or rational numbers).

A set S of integers is Diophantine precisely if there is some polynomial with integer coefficients f (n, x1, ..., xk) such that an integer n is in S if and only if there exist some integers x1, ..., xk …