MathDB

number of ways of writing 14 as product of 2 elements of set: a+13bi, a,b in Z

Source: Spanish Mathematical Olympiad 1989 P5

August 2, 2018

complex numbersnumber theory

Problem Statement

Consider the set

D

of all complex numbers of the form

a+b\sqrt{-13}

with

a,b \in Z

. The number

14 = 14+0\sqrt{-13}

can be written as a product of two elements of

D

14 = 2 \cdot 7

. Find all possible ways to express

14

as a product of two elements of

D