Solve the linear congruence for x : 34x≡51(mod85)
I found using the Euclidean Algorithm that the GCD is 17. Because the GCD evenly divides 51, there equivalence should be solvable. I made a Diophantine equation to solve: 34p−85q=17
From using the Euclidean Algorithm I have:
85=2⋅34+17
34=2⋅17+0
17=85−2⋅34
I do not know where to go from here in order to make this model the Diophantine equation in order to solve for p, and I'm not entirely sure what to do with the solution when I get it, because I am solving for x.
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