1985 OIM Problems/Problem 1
Problem
Find all triples of integers such that:
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
Square the first equation to get , and using the second equation
. Then with the elementary symmetric sums with three variables, their solutions are the solutions to the cubic
. With a little rational root bash and factoring we get
. Thus the integer solutions are the
.