On the number of special numbers
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, cilt.127, sa.3, ss.423-430, 2017 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 127 Sayı: 3
- Basım Tarihi: 2017
- Doi Numarası: 10.1007/s12044-016-0326-z
- Dergi Adı: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.423-430
- Anahtar Kelimeler: Special numbers, squarefull numbers, Thue-Mahler equations, abc conjecture, ABC-CONJECTURE
- Gazi Üniversitesi Adresli: Evet
Özet
For lack of a better word, a number is called special if it has mutually distinct exponents in its canonical prime factorizaton for all exponents. Let V(x) be the number of special numbers <= x. We will prove that there is a constant c > 1 such that V(x) similar to cx/log x. We will make some remarks on determining the error term at the end. Using the explicit abc conjecture, we will study the existence of 23 consecutive special integers.