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Do diophantine equations ax+by =C with gcd (a,b) = 1 have a solution?
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A linear diophantine equation is an algebraic equation in two or more variables where the coefficients and constant terms are integers. The solutions to these equations must also be integers.
To solve a linear diophantine equation, you can use a variety of methods such as substitution, elimination, or graphing. The goal is to find values for the variables that satisfy the equation while also being integers.
A linear diophantine equation is a type of linear equation where the coefficients and constants are restricted to integers. Linear equations, on the other hand, can have any real number as a coefficient or constant.
No, not all linear equations can be written as linear diophantine equations. Linear diophantine equations have the additional restriction of integer coefficients and constants, which is not present in all linear equations.
Linear diophantine equations can be used to solve problems involving number patterns, modular arithmetic, and integer solutions to real-world problems. They have applications in fields such as cryptography, engineering, and computer science.