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Интеллектуальная Система Тематического Исследования НАукометрических данных |
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Forbidden Integer Ratios of Consecutive Power Sumsстатья
- Авторы: Baoulina Ioulia N., Moree Pieter
- Сборник: From Arithmetic to Zeta-Functions: Number Theory in Memory of Wolfgang Schwarz
- Год издания: 2016
- Место издания: Springer International Publishing
- Первая страница: 1
- Последняя страница: 30
- DOI: 10.1007/978-3-319-28203-9_1
- Аннотация: Let S_k(m):=1^k+2^k+...+(m-1)^k denote a power sum. In 2011 Bernd Kellner formulated the conjecture that for m ≥ 4 the ratio S_k(m+1)/S_k(m) of two consecutive power sums is never an integer. We will develop some techniques that allow one to exclude many integers ρ as a ratio and combine them to exclude the integers 3 ≤ ρ ≤ 1501 and, assuming a conjecture on irregular primes to be true, a set of density 1 of ratios ρ. To exclude a ratio ρ one has to show that the Erdős-Moser type equation (ρ-1)S_k(m)=m^k has no non-trivial solutions.
- Добавил в систему: Баулина Юлия Николаевна