Square-Free Discriminants and Affect-Free Equations
نویسندگان
چکیده
منابع مشابه
Square-free discriminants of Frobenius rings
Let E be an elliptic curve over Q. It is well known that the ring of endomorphisms of Ep, the reduction of E modulo a prime p of ordinary reduction, is an order of the quadratic imaginary field Q(πp) generated by the Frobenius element πp. When the curve has complex multiplication (CM), this is always a fixed field as the prime varies. However, when the curve has no CM, very little is known, not...
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We say that a partial word w over an alphabet A is square-free if every factor xx of w such that x and x are compatible is either of the form ⋄a or a⋄ where ⋄ is a hole and a ∈ A. We prove that there exist uncountably many square-free partial words over a ternary alphabet with an infinite number of holes.
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In the article the formal characterization of square-free numbers is shown; in this manner the paper is the continuation of [19]. Essentially, we prepared some lemmas for convenient work with numbers (including the proof that the sequence of prime reciprocals diverges [1]) according to [18] which were absent in the Mizar Mathematical Library. Some of them were expressed in terms of clusters’ re...
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A word w is rich if it has |w| + 1 many distinct palindromic factors, including the empty word. A word is square-free if it does not have a factor uu, where u is a non-empty word. Pelantová and Starosta (Discrete Math. 313 (2013)) proved that every infinite rich word contains a square. We will give another proof for that result. Pelantová and Starosta denoted by r(n) the length of a longest ric...
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ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 1991
ISSN: 0387-3870
DOI: 10.3836/tjm/1270130487