七元一次不定方程整数解解公式

A Formula for Finding the Solutions of Linear Diophantine Equation in Seven Unknowns

讨论了七元一次不定方程一切整数解的解法.通过将不定方程的元进行结合,构造出3个三元一次不定方程,再利用三元一次不定方程的一切整数解的一个解公式,得到了其一切整数解的解公式,并讨论了其非负整数解解数问题.

The method of finding all solutions of a linear Diophantine equation in seven unknowns was discussed. Combining the elements of this Diophantine equation, three Diophantine equations in three unknowns were constructed. Finally, by using the formula of three unknowns, a formula of all solutions of this seven unknowns was given, and the number of nonnegative integer solutions was analyzed.