Question

Diaphontines equation explain pls

Answer 1

Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integral solutions are required. An Integral solution is a solution such that all the unknown variables take only integer values. Given three integers a, b, c representing a linear equation of the form : ax + by = c.

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Answer 2

Diophantine equation of degree 1 is easily solvable with little trial and error .

Degree 2 is also easy .

Degree 3 is tough and it is fairly tough .

Degree 4 is impossible to solve .

By the way what is meant by degree .

For example :

$x^3+x^2+x+1=0$ is an equation of degree 3 .

$x^2-6x+7$ is an equation of degree 2

A diophantine equation is a polynomial equation which has only and ONLY integer solutions nothing else .

For example :

$\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{x+y}=N$

Here this is a diophantine equation such that there exists only Integer solutions of x , y and z .

N is strictly a natural number here .

Strictly means strictly .

We cannot say that x / y / z has a  decimal value .

Diophantine equations can be solved with a simple trial and error but complex ones cannot be done so .

You have to plot graphs and then you have to take random values .

Some Diophantine equations cannot be solved without a computer.