[Number Theory] Pretty Easy, But Not That Easy

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Hello professor, I have a challenge for you. I have not found all the solutions to this equation yet. My father is a university professor in technology and he didn’t know its solution yet. It was in the Mathematics Olympiad in Morocco in the past. I found the solution (2;3) using Euclidean division by x-2... The important thing is that I wish I knew the solution from you. It is said that this equation was used for the first time in the chemical calculation of classical medicines.
Please can you? ❤❤

anaslmgader