MathDB

c is divisible by 5 in quasi-pythagorean triplet

Source: Baltic Way 1998

January 11, 2011

number theory proposednumber theory

Problem Statement

A triple

(a,b,c)

of positive integers is called quasi-Pythagorean if there exists a triangle with lengths of the sides

a,b,c

and the angle opposite to the side

c

equal to

120^{\circ}

. Prove that if

(a,b,c)

is a quasi-Pythagorean triple then

c

has a prime divisor bigger than

5