GENERAL SOLUTION OF LINEAR DIOPHANTINE EQUATION IN N UNKNOWNS AND APPLICATION OF LINEAR DIOPHANTINE EQUATION IN 2 UNKNOWNS OVER ZN

In present paper, we study the most important concept in number theory “Linear Diophantine Equation in n Unknowns”. Necessary and sufficient condition for the existence of solution and general the solution of linear Diophantine equation in n unknowns. We use the linear Diophantine equation in 2 unknowns in ring Zn to find the divisor, common divisor. We express a linear Diophantine equation over Zn in two unknowns and find the necessary and sufficient condition for the existence of solution of linear Diophantine equation and to find the solution over Zn