# Remembering Arithmetica!!!

**Number Theory**Level 4

Determine the sum of all possible positive integer values of \(x\) and \(y\) in the following Diophantine equation-\[54x+21y=906\] Note- Note that the question asks for the sum of only the positive integer values. If there is a common value of \(x\) and \(y\) in two solutions then you have to add them separately. For example- Say 1 set of solution is \(a,b\) and the other is \(b,c\) then their sum is \(2b+a+c\). This applies for a common value of \(x,y\) in a single set of solution.