Vladimir I. Arnold

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The Frobenius number of vector a, whose components as are natural numbers (having no common divisor greater than 1), is the minimal integer N (a) which is representable as a sum of the components as with nonnegative multiplicities, together with all the greater integers (like for N (4, 5) = 12). The mean Frobenius number is the arithmetical mean value of(More)
The multiplication by a constant (say, by 2) acts on the set Z/nZ of residues (mod n) as a dynamical system, whose cycles relatively prime to n all have a common period T (n) and whose orbits consist each of T (n) elements, forming a geometrical progression or residues. The paper provides many new facts on the arithmetical properties of these periods and(More)
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