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- W2334910327 abstract "kn + 1, and the integer kn + i = tn! + i, i = 2,..., n 1, is divisible by i and is thus composite. To prove that there exists a largest integer n to which each of its composite totitives can be added to obtain a composite, note first that for n large there exist primes p such that n +p* 0, the inequalities (9) hold with c3 = 1 + e, c4 = 1 E, for all sufficiently large n. This in turn provides the existence of a primep in the interval [n +p*, 2n] such thatp n -O (modp*). Since n <p < 2n, c =p n is a positive composite integer such that c < n and (c, n) = 1. Thus c is a composite totitive of n satisfying n + c =p a prime. The theorem follows since this can be achieved for all large n." @default.
- W2334910327 created "2016-06-24" @default.
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- W2334910327 date "1978-11-01" @default.
- W2334910327 modified "2023-09-28" @default.
- W2334910327 title "Hoover's Problem" @default.
- W2334910327 cites W4213214460 @default.
- W2334910327 doi "https://doi.org/10.1080/0025570x.1978.11976731" @default.
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