KaydedilenlerDerginizi ekleyin

Dergiler / Turkish Journal of Mathematics / 2005 / Cilt: 29 - Sayı: 2

On the Value Set of n! Modulo a Prime

Florian LUCA
William D. BANKS
Igor E. SHPARLINSKI
Henning STICHTENOTH
Sayfa
169–174
Yayın Tarihi
2022-11-05
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We show that for infinitely many prime numbers p there are at least \log\log p / \log\log\log p distinct residue classes modulo p that are not congruent to n! for any integer n.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We show that for infinitely many prime numbers p there are at least \log\log p / \log\log\log p distinct residue classes modulo p that are not congruent to n! for any integer n.
📊
Temel Bulgular & Veri:We show that for infinitely many prime numbers p there are at least \log\log p / \log\log\log p distinct residue classes modulo p that are not congruent to n! for any integer n.
💡
Sonuç & Katkı:We show that for infinitely many prime numbers p there are at least \log\log p / \log\log\log p distinct residue classes modulo p that are not congruent to n! for any integer n.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Turk. J. Math. · (2005) · 169-174. Full text: pdf Other articles published in the same issue: Turk. J. Math.

Özet

We show that for infinitely many prime numbers p there are at least \log\log p / \log\log\log p distinct residue classes modulo p that are not congruent to n! for any integer n.

Abstract

We show that for infinitely many prime numbers p there are at least \log\log p / \log\log\log p distinct residue classes modulo p that are not congruent to n! for any integer n.

🔖

Bu Makaleye Atıf Yap

LUCA, F., BANKS, W. D., SHPARLINSKI, I. E., STICHTENOTH, H. (2022). On the Value Set of n! Modulo a Prime. Turkish Journal of Mathematics, Cilt: 29 - Sayı: 2, 169–174. https://ajindex.com/articles/608731

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (4)

  1. C. Cobeli, M. Vˆajˆaitu and A. Zaharescu, ‘The sequence n (mod p)’, J. Ramanujan Math. Soc., 15 (2000), 135–154. M. Z. Garaev and F. Luca, “Character sums and factorials modulo p”, to appear in J. Theorie Nombres, Bordeaux. M. Z. Garaev, F. Luca and I. E. Shparlinski, ‘Character sums and congruences with n ’, Trans. Amer. Math. Soc., (to appear). M. Z. Garaev, F. Luca and I. E. Shparlinski, ‘Exponential sums and congruences with factorials’, J. Reine Angew. Math., 356 (2004), 5089-5102.
  2. R. K. Guy, Unsolved problems in number theory, Springer-Verlag, New York, 1994.
  3. J. C. Lagarias, H. L. Montgomery and A. M. Odlyzko, ‘A bound for the least prime ideal in the Chebotarev density theorem’, Invent. Math., 54 (1979), 271–296. F. Luca and P. St˘anic˘a, ‘Products of factorials modulo p’, Colloq. Math., 96 (2003), 191–205.
  4. D. A. Marcus, Number fields, Springer-Verlag, 1977. G. P´olya and G. Szeg¨o, Problems and theorem in analysis, Vol.II, Springer-Verlag, 1976. B. Rokowska and A. Schinzel, ‘Sur une probl´eme de M. Erd˝os’, Elem. Math., 15 (1960), 84–85.