Competition problem — Number theory

Library / /3 of 520

Number theory Difficulty 4.7 AIME Find the answer

13. Given positive integers $x, y, z$ satisfying $x y + 1000 z = 2020$ , then $(x, y, z)$ has $\qquad$ groups.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

$3$

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.