Geodesic
On a Theorem of Sylvester and Schur
Canadian mathematical bulletin, Tome 16 (1973) no. 2, pp. 195-199

Voir la notice de l'article provenant de la source Cambridge University Press

In 1892, Sylvester [7] proved that in the set of integers n, n+l,..., n+k—1, n> k > 1, there is a number containing a prime divisor greater than k. This theorem was rediscovered, in 1929, by Schur [6]. More recent results include an elementary proof by Erdös [1] and a proof of the following theorem by Faulkner [2]: Let pk be the least prime ≥2k; if n≥pk then has a prime divisor ≥pk with the exceptions and In that paper the author uses some deep results of Rosser and Schoenfeld [5] on the distribution of primes. 
Hanson, D. On a Theorem of Sylvester and Schur. Canadian mathematical bulletin, Tome 16 (1973) no. 2, pp. 195-199. doi: 10.4153/CMB-1973-035-3
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[1] 1. Erdös, P., A theorem of Sylvester and Schur, J. London Math. Soc. 9 (1934), 282–288. Google Scholar

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[3] 3. Hanson, D., On the product of the primes, Canad. Math. Bull., (1) 15 (1972), 33–37. Google Scholar

[4] 4. Moser, L., Insolvability of , Canad. Math. Bull. (2) 6 (1963), 167–169. Google Scholar

[5] 5. Rosser, J.B. and Schoenfeld, L., Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64–94. Google Scholar

[6] 6. Schur, I., Einige Satze uber Primzahlen mit wendung auf Irreduzibilitatsfragen, Sitzungberichte der preussichen Akedemie der Wissenschaften, Phys. Math. Klasse, 23 (1929), 1–24. Google Scholar

[7] 7. Sylvester, J.J., On arithmetical series, Messenger of Mathematics, XXI (1892), 1–19, 87–120, and Mathematical Papers, 4 (1912), 687–731. Google Scholar

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