Читать книгу Writings of Charles S. Peirce: A Chronological Edition, Volume 8 - Charles S. Peirce - Страница 27

13

Note on Pythagorean Triangles

c. 1890

Houghton Library

A Pythagorean triangle is a set of 3 integer numbers proportional to the legs and hypotheneuse of a right triangle. It is irreducible if the 3 integers have no common measure. The number of irreducible Pythagorean triangles of which a given number is hypotheneuse is 0, if the number contains a prime factor not of the form (4n + 1); otherwise, it is equal to 2^{p − 1} where p is the number of its different prime factors. For example, 725 = 5² · 29. Accordingly,

It is also true that (500)² + (525)² = (725)²; but that triangle is reducible. Again, 1105 = 5 · 13 · 17. Accordingly,