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welcome the next topic topic end Diophantine equations this ones kind of exciting and for newer students a little bit challenging but after a few examples hopefully it wont be too bad alright the first video and one is just an introduction to linear Diophantine equations then the next videos well have some examples where we solve problems alright first of all what is a linear Diophantine equation its an equation of this form ax was b y equals C were the solutions X comma Y the solutions X comma Y are integers hence thats what makes it in the number theory subset alright Diophantus of Alexandria he lived from 200 to 280 for AD sometimes hes referred to as the father of algebra and he studied these types of equations hence the name all right first of all these died upon same linear equations are solvable if and only if youll find in later math classes iff stands for that if an awliya the greatest common divisor of any M be divided C and Ill give you an example Ill write it here