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Solutions of the congruence 1 + 2 f ( n ) + ⋯ + n f ( n ) ≡ 0 mod n
Author(s) -
Grau José María,
Moree Pieter,
OllerMarcén Antonio M.
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500057
Subject(s) - mathematics , congruence (geometry) , prime (order theory) , pure mathematics , combinatorics , geometry
In this paper we characterize, in terms of the prime divisors of n , the pairs ( k , n ) for which n divides∑ j = 1 n j k . As an application, we derive some results on the setsM f : = n ≥ 1 : f ( n ) > 1 and ∑ j = 1 n j f ( n ) ≡ 0modnfor some choices of f .
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