منابع مشابه
Note on primitive permutation groups and a diophantine equation
If a group G has a maximal subgroup H, tl-.en G acts by right multiplication on the set fi of right cosets of H in G as a primitive, but not necessarily faithful, permutation group. As part of the search for new finite simple groups it is of interest to determine all possible groups G, and in particular all simple groups, which contain a given group H as a maximal subgroup. This problem is very...
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Introduction. Diophantus noted that the rational numbers 1/16, 33/16, 17/4 and 105/16 have the following property: the product of any two of them increased by 1 is a square of a rational number (see [2, 3]). Let n be an integer. A set of positive integers {a1, a2, . . . , am} is said to have the property D(n) if aiaj + n is a perfect square for all 1 ≤ i < j ≤ m. Such a set is called a Diophant...
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Given a set of nonnegative real numbers Λ= {λi}i=0, a Λ-polynomial (or Müntz polynomial) is a function of the form p(x)=ni=0 aizi (n∈N). We denote byΠ(Λ) the space of Λ-polynomials and byΠZ(Λ) := {p(x)=ni=0 aizi ∈Π(λ) : ai ∈ Z for all i≥ 0} the set of integral Λ-polynomials. Clearly, the sets ΠZ(Λ) are subgroups of infinite rank of Z[x] wheneverΛ⊂N, #Λ=∞ (by infinite rank, wemean that the real ...
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The wish to determine the complete set of rational integral solutions of (1) was expressed by Diaconis and Graham in [2, p. 328]. Apparently, the solutions to this diophantine problem correspond to values of keN for which the Radon transform based on the set of all xeZ\ with exactly four ones is not invertible. We thank Hendrik Lenstra who communicated the problem to Jaap Top, to whom we are eq...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2003
ISSN: 0022-314X
DOI: 10.1016/s0022-314x(02)00055-0