What is the integer solution?

An integer solution is a solution such that all the unknowns take integer values). Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations.

How do you know if a Diophantine equation has no solution?

Applied to the simplest Diophantine equation, ax + by = c, where a, b, and c are nonzero integers, these methods show that the equation has either no solutions or infinitely many, according to whether the greatest common divisor (GCD) of a and b divides c: if not, there are no solutions; if it does, there are …

How do you find integers?

To calculate the number of integers, find subtract the integers of interest and then subtract 1. As a proof of concept, calculate the number of integers that fall between 5 and 10 on a number line. We know there are 4 (6, 7, 8, 9).

How many solutions does a Diophantine equation have?

In the example above, an initial solution was found to a linear Diophantine equation. This is just one solution of the equation, however. When integer solutions exist to an equation a x + b y = n , ax+by=n, ax+by=n, there exist infinitely many solutions.

What is meant by Diophantine equation?

In mathematics, a Diophantine equation is a polynomial equation, usually involving two or more unknowns, such that the only solutions of interest are the integer ones (an integer solution is such that all the unknowns take integer values).

Does an equation have integer solutions?

Integer solutions to an equation means solutions which are in the set of integers (see first line of my answer). The problem (x+3)(x-1) = 0 has two integer solutions, namely x=-3 and x=1. Try plugging them into the equation and you will see they make it true. So, since they are integers they are integer solutions.

How do you calculate integers on a calculator?

When you are using a calculator to solve for integers, you will use the “-” sign found on all scientific calculators to solve for negative integers. Determine if you are adding, subtracting, dividing or multiplying a positive or negative integer. Locate the “-” sign on your calculator.

Who Solved Diophantine equation?

The equation was eventually solved by Euler in the early 18th century, who also solved a number of other Diophantine equations. The smallest solution of this equation in positive integers is x = 226153980, y = 1766319049 (see Chakravala method).