Integer triangles

An integer triangle is a triangle with side lengths $a$, $b$, and $c$, where $a$, $b$, and $c$ are positive integers and satisfy the triangle inequalities: $a + b > c$, $a + c > b$, $b + c > a$.

Important properties

• All sides are positive integers.

• The triangle inequalities must be satisfied.

• Special cases include Pythagorean triangles (right triangles with integer sides).

• There are infinitely many integer triangles.