CAYLEY 2019 Problem 25

Past Contests CAYLEY CAYLEY - 2019
1

For how many positive integers x does there exist a rectangular prism P Q R S T U V W, labelled as shown, with P R=1867, P V=2019, and P T=x ?

Image

Answer Choices
A. 1980
B. 1982
C. 1984
D. 1983
E. 1981