Diophantine equation is one of the oldest branches of number theory. Diophantine in ancient Greece began to study indefinite equations as early as the 3rd century AD, so indefinite equations are often called Diophantine equations. Diophantine, an ancient Greek, is recognized as the originator of algebra, and there are not many stories about his life. Today, we call the indefinite equation with integral coefficients "Diophantine equation", and the main content is to discuss its integer solution or rational number solution. He has three books, the most famous of which is Arithmetic, which contains 189 questions and their answers, and many of them are indefinite equations (the number of variables is greater than the number of equations) or indefinite equations (more than two variables). Diophantine only considers positive understanding, and indefinite equations usually have infinite solutions.

There are three problems to be solved in learning indefinite equations: (1. Determine when there is a solution. 2. Determine the number of solutions when there are solutions. 3. Find all the solutions. ) China was the first country to study indefinite equations, and the problem of five * * * wells at the beginning of A.D. was an indefinite equations problem. In the 5th century, China made a systematic study on the theory of indefinite equations. Qin's "great solution" links indefinite equations with congruence theory. A hundred chickens asked, "Chicken Weng 1, straight money 5, chicken mother 1, straight money 3, chicken chicks 3, straight money 1." One hundred dollars to buy a hundred chickens, ask the chicken, mother, chick geometry? Let x, y and z represent the number of chickens, females and chicks respectively, then this problem is the non-negative integer solution x, y and z of indefinite equations, which is a ternary indefinite equations problem.

The life of Diophantine

Diophantine, the father of algebra, was a great mathematician in ancient Greece. He was the first person who knew how to use symbolic representation to study problems. Among them, Diophantine is probably the most famous epitaph:

"Surprisingly, Diophantine was buried in the grave. It faithfully records the road it has experienced.

God gave me one sixth of my childhood, one twelfth of my childhood and one seventh of my childhood, and lit the wedding candle.

Five years later, the blessed son, Ning Xiner, who was poor and backward, died at half the age of his father and entered a cold grave.

Sadness can only be made up by studying number theory. Four years later, he has also completed the journey of life. 」

It can be seen from this: "In Diophantu's life, childhood accounted for 1/6, and youth accounted for112. I spent 1/7 before I got married, and I was born five years later. His father died four years later, and his life expectancy was half that of his father. " The equation for calculating Diophantine is X/6+X/ 12+X/7+5+X/2+4 = X, so we know that Diophantine died at the age of 84.