Is Diophantine equation solvable?
For instance, we know that linear Diophantine equations are solvable.
How many solutions are there to the Diophantine equation?
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 …
What is the purpose of Diophantine equation?
The purpose of any Diophantine equation is to solve for all the unknowns in the problem. When Diophantus was dealing with 2 or more unknowns, he would try to write all the unknowns in terms of only one of them.
Who discovered Diophantine equation?
Diophantus of Alexandria
The first known study of Diophantine equations was by its namesake Diophantus of Alexandria, a 3rd century mathematician who also introduced symbolisms into algebra. He was author of a series of books called Arithmetica, many of which are now lost.
Which of the following Diophantine equation is not solvable?
gcd(6, 51) = 3Hence the equation is not solvable. gcd(33, 14) = 1.
What is x3 y3 z3 K?
The equation x3+y3+z3=k is known as the sum of cubes problem. While seemingly straightforward, the equation becomes exponentially difficult to solve when framed as a “Diophantine equation” — a problem that stipulates that, for any value of k, the values for x, y, and z must each be whole numbers.
What is the linear Diophantine equation?
A Linear Diophantine equation (LDE) is an equation with 2 or more integer unknowns and the integer unknowns are each to at most degree of 1. Linear Diophantine equation in two variables takes the form of ax+by=c, where x,y∈Z and a, b, c are integer constants.
What is Diophantine analysis?
or Diophantine analysis noun Mathematics. any of several methods for finding integral solutions for equations with more than one variable whose coefficients are integers.
Which of the following diophantine equations Cannot be solved?
Expert Answer The diophantine equations are of the form ax+by=c, if c can be divided by the greatest common divisor (gcd) of a and b then this equation has integer solutions. 22 cannot be divided by 3 without forming fractions, so this equation doesn’t have any solutions.