1. piccard-little theorem (piccard-Lindel? F theorem)

For a given initial value problem, if the derivative of the function satisfies Lipshits condition, there is a unique solution in a certain interval. Lee's condition requires that the derivative of a function does not change more than a multiple of a constant in a given interval.

This theorem has important application value in the study of differential equations, which ensures the existence and uniqueness of solutions to initial value problems and provides a basis for the study of differential equations. The applicable condition of Picard-Little theorem is that the derivative of the function satisfies Lipshits condition. Lee's condition requires that the derivative of a function does not change more than a multiple of a constant in a given interval.

Second, Bezu Theorem (bézout's Theorem)

Bezu Theorem (also called Peshu Theorem) is a theorem about the greatest common divisor, named after the French mathematician Etienne Peshu.

For any integer A, B and their greatest common divisor D, there are integers X and Y, so ax+by=d holds. For any integer A and B and their greatest common divisor D, there are integers X and Y, so ax+by is a multiple of D. When A and B are coprime, that is, their greatest common divisor is 1, there are integers X and Y, which makes ax+by= 1 hold.

Third, Fermat's last theorem.

Fermat's Last Theorem is a mathematical problem put forward by Pierre de Fermat, a French mathematician in the17th century. Its expression is x n+y n = z n, where n is greater than 2 and there is no positive integer solution.

Fermat wrote this assertion in the margin of a book, but did not give proof. This problem has aroused the interest of many mathematicians and promoted the development of number theory. After more than three centuries' efforts, Fermat's Last Theorem was finally proved by the British mathematician andrew wiles in 1995.

4. Pythagorean theorem.

Pythagorean theorem, also known as Pythagorean theorem, is a basic geometric theorem. It points out that in a right triangle, the sum of squares of right angles is equal to the square of hypotenuse 1. Specifically, if the lengths of two sides of a triangle are A and B, respectively, and the length of the hypotenuse is C, then according to Pythagoras theorem, there is a? + b？ = c？ .

Five, euler theorem (Euler's)

Is a number theory theorem about congruence, also known as Fermat-euler theorem or Euler function theorem. It is a generalized form of Fermat's theorem. Euler theorem showed that if positive integers A and N are coprime (that is, the greatest common divisor is 1), the Euler function value φ(n) of A satisfies the following congruence relation: A φ (n) ≡ 1 (mod n).