MathNet 2024-part-03 — 168 problems (EN–VI) Question 56

Determine the number of pairs $(m, n)$ of integers with absolute value less than $10000$ that solve the equation $n^{2}+2024 n+2024 m=2024$.

(A) 4
(B) 9
(C) 10
(D) 18
(E) 19