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Topic	Hey math nerds, where should I go next?
lderivedx 05/05/24 2:15:36 AM #44:	Pretty sure p=~~1013.~~ Since 2027 is prime, the multiplicative group of integers modulo 2027 has order 2026, which has prime factorization 21013. If such a p exists, this means the cyclic subgroup generated by the element 2024^p must divide 2026, and so p must be either 2 or 1013. We can check that 2 doesn't work: 2024^2 - 2023^2 = 2024+2023 = 4047, which is not a multiple of 2027. Thus if p exists it must be 1013. Not sure how I'd verify this p by hand but WolframAlpha confirms it. --- i cant get off unless we're violating at least four OSHA regulations* <cite>lderivedx posted [p:980246796] in Hey math n... [t:80759838]...</cite> <quote>Pretty sure p=1013.Since 2027 is prime, the multiplicative group of integers modulo 2027 has order 2026, which has prime factorization 2*1013. If such a p exists, this means the cyclic subgroup generated by the element 2024^p must divide 2026, and so p must be either 2 or 1013. We can check that 2 doesn't work: 2024^2 - 2023^2 = 2024+2023 = 4047, which is not a multiple of 2027. Thus if p exists it must be 1013. Not sure how I'd verify this p by hand but WolframAlpha confirms it. --- i cant get off unless we're violating at least four OSHA regulations</quote> ... Copied to Clipboard!
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