Dodo said:Start with a simpler equation, ax+d, and then try to add the other terms one by one.
Well, yes! It's an equation! ax+ by+ cz+ d isn't an equation.ACardAttack said:I goofed...it is actually ax+by+cz=d...does that make a difference?
To prove a Diophantine equation, you need to show that there exists at least one solution that satisfies all the given conditions. This can be done through various methods such as substitution, elimination, or using modular arithmetic.
A Diophantine equation is an algebraic equation where the solutions are restricted to integers only. It is named after the ancient Greek mathematician Diophantus who studied these types of equations.
No, not all Diophantine equations can be solved. Some equations have no solutions, while others may have infinitely many solutions. The difficulty of solving a Diophantine equation depends on the complexity of the equation and the techniques used to solve it.
Diophantine equations have various applications in fields such as cryptography, number theory, and computer science. They are used to solve problems related to finding integer solutions to equations, calculating the number of solutions, and determining patterns in the solutions.
Yes, there are several famous unsolved Diophantine equations, including Fermat's Last Theorem, the Catalan's Conjecture, and the Goldbach's Conjecture. These equations have been studied for centuries and continue to intrigue mathematicians with their elusive solutions.