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Задача по теории чисел с прошедшей недавно Санкт-Петербургской олимпиады!

Дано натуральное число m. Докажите, что существует бесконечно много натуральных n, взаимно простых с m, для которых (n!)^2+1 — составное.



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#задача #теория_чисел
Задача по теории чисел с прошедшей недавно Санкт-Петербургской олимпиады!

Дано натуральное число m. Докажите, что существует бесконечно много натуральных n, взаимно простых с m, для которых (n!)^2+1 — составное.

BY JustScience | Олимпиадная Математика




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The messaging service and social-media platform owes creditors roughly $700 million by the end of April, according to people briefed on the company’s plans and loan documents viewed by The Wall Street Journal. At the same time, Telegram Group Inc. must cover rising equipment and bandwidth expenses because of its rapid growth, despite going years without attempting to generate revenue.

For some time, Mr. Durov and a few dozen staffers had no fixed headquarters, but rather traveled the world, setting up shop in one city after another, he told the Journal in 2016. The company now has its operational base in Dubai, though it says it doesn’t keep servers there.Mr. Durov maintains a yearslong friendship from his VK days with actor and tech investor Jared Leto, with whom he shares an ascetic lifestyle that eschews meat and alcohol.

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