← Back to Test

Problem 2 - Entrance Test

How many integers n satisfy 1 ≤ n ≤ 2024 and n² ≡ 1 (mod 2024)?

Correct: A

2024=8·11·23. Use CRT. Mod 8: n²≡1 ⇒ n≡1,3,5,7 (4 choices). Mod 11: n²≡1 ⇒ n≡±1 (2 choices). Mod 23: n²≡1 ⇒ n≡±1 (2 choices). Total solutions=4·2·2=16.