MathDB

13

Part of 2024 AIME

Problems(2)

Prime Squared

Source: 2024 AIME I #13

2/2/2024
Let pp be the least prime number for which there exists a positive integer nn such that n4+1n^{4}+1 is divisible by p2p^{2}. Find the least positive integer mm such that m4+1m^{4}+1 is divisible by p2p^{2}.
AMCAIMEAIME I
2023 AIME II P8 all over again

Source: 2024 AIME II Problem 13

2/8/2024
Let ω≠1\omega \ne 1 be a 1313th root of unity. Find the remainder when ∏k=012(2−2ωk+ω2k) \prod_{k=0}^{12} \left(2 - 2\omega^k + \omega^{2k} \right) is divided by 10001000.
AIMEAIME IAIME II