Proof that Weber’s normal units are not perfect powers
نویسندگان
چکیده
منابع مشابه
Perfect Powers That Are Sums of Consecutive Cubes
Euler noted the relation 63= 33+43+53 and asked for other instances of cubes that are sums of consecutive cubes. Similar problems have been studied by Cunningham, Catalan, Gennochi, Lucas, Pagliani, Cassels, Uchiyama, Stroeker and Zhongfeng Zhang. In particular, Stroeker determined all squares that can be written as a sum of at most 50 consecutive cubes. We generalize Stroeker’s work by determi...
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A common task in phylogenetics is to find an evolutionary tree representing proximity relationships between species. This motivates the notion of leaf powers: a graph G = (V,E) is a leaf power if there exist a tree T on leafset V and a threshold k such that uv ∈ E if and only if the distance between u and v in T is at most k. Characterizing leaf powers is a challenging open problem, along with ...
متن کاملPerfect Matchings and Perfect Powers
In the last decade there have been many results about special families of graphs whose number of perfect matchings is given by perfect or near perfect powers (N. Elkies et al., J. Algebraic Combin. 1 (1992), 111– 132; B.-Y. Yang, Ph.D. thesis, Department of Mathematics, MIT, Cambridge, MA, 1991; J. Propp, New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999). In this pa...
متن کاملOn powers that are sums of consecutive like powers
1 Background The problem of cubes that are sums of consecutive cubes goes back to Euler ([10] art. 249) who noted the remarkable relation 33 + 43 + 53 = 63. Similar problems were considered by several mathematicians during the nineteenth and early twentieth century as surveyed in Dickson’sHistory of the Theory of Numbers ([7] p. 582–588). These questions are still of interest today. For example...
متن کاملSparse Perfect Powers
We examine the problem of detecting when a given sparse polynomial f is equal to hr for some other polynomial h and integer r ≥ 2. In this case we say f is a perfect power, and h is its r th root. We give randomized algorithms to detect when f is a perfect power, by repeatedly evaluating the polynomial in specially-chosen finite fields and checking whether the evaluations are themselves perfect...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1961
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1961-0133317-4