Pythagorean theorem holds for positive integers, that is, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of two right-angled sides. The answer to the question whether the Pythagorean number must be an integer is not necessarily. In fact, there are some Pythagorean triples, in which the lengths of two right angles and the length of the hypotenuse are rational numbers, but they are not integers. Mathematically, these triples are called irrational Pythagorean triples. For example, the pythagorean number can be 3, 4, 5, 5/3, 4/3, 25/9, all of which satisfy the pythagorean theorem. However, it should be noted that the hypotenuse length and right-angled side length of most right-angled triangles cannot be rational numbers at the same time, that is, in most cases, the pythagorean number is an integer.

Pythagorean theorem is widely used in mathematics, physics, engineering and other fields. It can be used to calculate the side length, area, perimeter and position of a triangle. In addition, Pythagorean theorem is also an important mathematical theoretical basis in modern digital communication technology, which is widely used in signal detection and signal processing.