aspg-21-1986-1791468632 20261008141032 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2023 21 4 Hasan Sankari Tishreen University, Department Of Mathematics, Latakia, Syria Mohammad Abobala Tishreen University, Department Of Mathematics, Latakia, Syria First Von Shtawzen's Diophantine equation is a non-linear Diophantine equation with three variables . This equation has been conjectured that it has a finite number of integer solutions, and this number of solutions is divisible by 6. Second Von Shtawzen's Diophantine equation is a non-linear Diophantine equation with four variables. This equation has been conjectured that it has a finite number of integer solutions, and this number of solutions is divisible by 8. In this paper, we prove that first Von Shtawzen's conjecture is true, where we show that first Von Shtawzen's Diophantine equations has exactly 12 solutions. On the other hand, we find all solutions of this Diophantine equations. In addition, we provide a full proof of second Von Shtawzen's conjecture, where we prove that the previous Diophantine equation has exactly 16 solutions, and we determine all of its possible solutions 2023 146 154 1986 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.210414 https://www.americaspg.com/journal/21/article/1986 https://www.americaspg.com/storage/51737489231.pdf