Arithmetic problems of plane geometry

three positive integers, the squares of two of which sum to the square of the third

triangle that has side lengths and area that are all integers

positive integer that is the area of a right triangle with three rational number sides

triangle with integer side lengths

non-existence proof in number theory, the only complete proof left by Pierre de Fermat

four integers where the sum of the squares of three equal the square of the fourth

infinite set of points in R2 with mutual integer distances must be a straight line

set of integers, the lengths of the sides of a triangle with a 60° angle

cyclic pentagon whose side lengths and area are all rational numbers