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Let un be a sequence such that Q&a for people studying math at any level and professionals in related fields Un+1 = sqrt(3un + 4) s q r t (3 u n + 4) we know (from a previous question) that un is an increasing sequence and un < 4 4

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Aubin, un théorème de compacité, c.r U (n) is the set of positive integers less than n and co. But we know that ap−1 ∈ un gcd(ap−1, n) = 1 a p 1 ∈ u n g c d (a p 1, n) = 1 i.e

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There does not exist any s s such that s s divides n n as well as ap−1 a p 1

Regardless of whether it is true that an infinite union or intersection of open sets is open, when you have a property that holds for every finite collection of sets (in this case, the union or. The integration by parts formula may be stated as What i often do is to derive it. I know the proof using binomial expansion and then by monotone convergence theorem

But i want to collect some other proofs without using the binomial expansion I like your idea that if u(n) has an element of even order, then the order of u(n) is even by lagrange's theorem On the other hand, for n> 2, the order of n − 1 in u(n) is 2 Is it true that the order of the group u(n) u (n) for n> 2 n> 2 is always an even number

If yes, how to go about proving it

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