On the matricial version of Fermat–Euler congruences
Arnold, Vladimir (2006), On the matricial version of Fermat–Euler congruences, Japanese Journal of Mathematics, 1, 1, p. 1-24. http://dx.doi.org/10.1007/s11537-006-0501-6
TypeArticle accepté pour publication ou publié
Journal nameJapanese Journal of Mathematics
MetadataShow full item record
Abstract (EN)The congruences modulo the primary numbers n=p a are studied for the traces of the matrices A n and A n-φ(n), where A is an integer matrix and φ(n) is the number of residues modulo n, relatively prime to n. We present an algorithm to decide whether these congruences hold for all the integer matrices A, when the prime number p is fixed. The algorithm is explicitly applied for many values of p, and the congruences are thus proved, for instance, for all the primes p ≤ 7 (being untrue for the non-primary modulus n=6). We prove many auxiliary congruences and formulate many conjectures and problems, which can be used independently.
Subjects / KeywordsEuler zeta function; Euler group; little Fermat Theorem; geometric progression; arithmetical turbulence
Showing items related by title and author.