What do you mean by "a(n), b(n) (and so, c(n))" ?danieldf said:a(3b+1)=c
The solutions are obvious. I want to know if there is a solution a(n), b(n) (and so, c(n)) or at least a solution a(b).
Can someone help with that..?
There are an infinite number. The only comprehensive one of all possibilities though isdanieldf said:I mean a solutions in one variable. Like (2n, n²-1,n²+1) is a solutioin for x²+y²=z²
A Diophantine equation is a polynomial equation with integer coefficients and solutions that are also integers. It was first studied by the ancient Greek mathematician Diophantus.
In this equation, a, b, and c are all integers. The equation is saying that the product of a and the expression (3b+1) is equal to c.
The goal when solving a Diophantine equation is to find all possible integer solutions for the variables in the equation. This can be a difficult task, and in some cases, there may be an infinite number of solutions.
Yes, there are several techniques for solving Diophantine equations, including factoring, substitution, and using modular arithmetic. The method used will depend on the specific equation and the available information.
Yes, there are some Diophantine equations that have no integer solutions. For example, the equation x^2 + y^2 = 3 has no solutions because the sum of two squares cannot equal 3. This is known as Fermat's Last Theorem.