منابع مشابه
What Is a Closed-Form Number?
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متن کاملEach Natural Number Is of the Form X
In this paper we prove that any natural number n can be written as x + y + Tz with x, y, z ∈ Z and Tz = z(z + 1)/2. Also, we can express n in any of the following forms: x + y + 2Tz , x 2 + 2y + Tz , x 2 + 2y + 2Tz , x 2 + 2y + 4Tz , x + 2Ty + 2Tz , x 2 + 4Ty + Tz , x 2 + 4Ty + 2Tz , 2x + Ty + Tz , 2x 2 + 2Ty + Tz , 2x 2 + 4Ty + Tz , Tx + 4Ty + Tz , 2Tx + 2Ty + Tz , 2Tx + 4Ty + Tz . Concerning ...
متن کاملHarmonic number sums in closed form
We extend some results of Euler related sums. Integral and closed form representation of sums with products of harmonic numbers and cubed binomial coefficients are developed in terms of Polygamma functions. The given representations are new. AMS subject classifications: Primary 11B65; Secondary 33C20
متن کاملSolving resultant form equations over number fields
We give an efficient algorithm for solving resultant form equations over number fields. This is the first time that such equations are completely solved by reducing them to unit equations in two variables.
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ژورنال
عنوان ژورنال: Nexus Network Journal
سال: 2005
ISSN: 1590-5896,1522-4600
DOI: 10.1007/s00004-005-0013-3