Here's the question:

From these congruences, I can writeQuote:

Determine the value of , if satisfies:

From which we get that

Ergo,

Now, I managed to find different values forpandkthrough trial and error so that the left side and right side of the equation become the same number (which is 14). And that's the answer for the question.

But my question is: isn't this possible to do algebraically or at least numerically rather than through trial and error?

Correct me if I am wrong; but isn't this a Diophantine equation which has to be solved with Euclides algorithm?

Thanks!