Sumsets without powerful numbers
نویسندگان
چکیده
منابع مشابه
The Power of Powerful Numbers
In this note we discuss recent progress concerning powerful numbers, raise new questions and show that solutions to existing open questions concerning powerful numbers would yield advancement of solutions to deep, long-standing problems such as Fermat's Last Theorem. This is primarily a survey article containing no new, unpublished results. A powerful number is a positive integer n which is div...
متن کاملArithmetic Progressions in Sumsets and Van der Waerden Numbers
We introduce the concepts of hereditary non-uniformity and restricted hereditary nonuniformity for subsets of Z/NZ, and prove theorems about such sets which imply various results about arithmetic progressions. In particular we show that if A is a subset of Z/NZ with size αN , where α ∈ (0, 1) is fixed, then A + A contains an arithmetic progression of length at least ec √ logN . This improves a ...
متن کاملNotes on geometry of numbers Progressions in sumsets
Let Λ be a lattice with basis x1, x2, . . . , xn. The fundamental parallellopiped of Λ with respect to x1, x2, . . . , xn is the set PΛ = {a1x1 + a2x2 + · · · + anxn : 0 ≤ ai < 1}. Note that the sets x + P , x ∈ Λ are disjoint and their union is R. The determinant det(Λ) of Λ is the volume of P , which is well-defined by the first lemma. Alternatively, det(Λ) is |det(A)|, where A = (x1, x2, . ....
متن کاملVoting without Version Numbers
Voting protocols are widely used to provide mutual exclusion in distributed systems and to guarantee the consistency of replicated data in the presence of network partitions. Unfortunately, the most efficient voting protocols require fairly complex metadata to assert which replicas are up-to-date and to denote the replicas that belong to that set. We present a much simpler technique that does n...
متن کاملLanguage: Life without Numbers
If your language did not have words for numbers, would you be able to think about numeric quantities? An Amazonian culture where number words are limited to one, two and many has provided new insights to the interaction between thought and language.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2007
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa130-4-7