On a decomposition of polynomials in several variables
One considers representation of a polynomial in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.
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Andrzej Schinzel (2002)
Journal de théorie des nombres de Bordeaux
One considers representation of a polynomial in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.
A. Schinzel (2002)
Colloquium Mathematicae
One considers representation of cubic polynomials in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.
D. Suryanarayana, R. Rama Chandra Rao (1973)
Mathematica Scandinavica
Christopher Hooley (1996)
Journal für die reine und angewandte Mathematik
Christopher Hooley (1986)
Journal für die reine und angewandte Mathematik
Thanigasalam, K. (1983/1984)
Portugaliae mathematica
Robertson, John P. (2006)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
Robertson, John P. (2009)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
A. Sarkozy, P. Erdos (1977)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Györy, K. (1993)
Mathematica Pannonica
Mollin, R.A., Walsh, P.G. (1986)
International Journal of Mathematics and Mathematical Sciences
Györy, K., Mignotte, M., Shorey, T.N. (1990)
Mathematica Pannonica
Fan Ge, Zhi-Wei Sun (2016)
Colloquium Mathematicae
For m = 3,4,... those pₘ(x) = (m-2)x(x-1)/2 + x with x ∈ ℤ are called generalized m-gonal numbers. Sun (2015) studied for what values of positive integers a,b,c the sum ap₅ + bp₅ + cp₅ is universal over ℤ (i.e., any n ∈ ℕ = 0,1,2,... has the form ap₅(x) + bp₅(y) + cp₅(z) with x,y,z ∈ ℤ). We prove that p₅ + bp₅ + 3p₅ (b = 1,2,3,4,9) and p₅ + 2p₅ + 6p₅ are universal over ℤ, as conjectured by Sun. Sun also conjectured that any n ∈ ℕ can be written as and 3p₃(x) + p₅(y) + p₇(z) with x,y,z ∈ ℕ; in...
Guang-Liang Zhou, Zhi-Wei Sun (2022)
Czechoslovak Mathematical Journal
We study sums and products in a field. Let be a field with , where is the characteristic of . For any integer , we show that any can be written as with and , and that for any we can write every as with and . We also prove that for any and there are such that .
K. Thanigasalam (1980)
Acta Arithmetica
J. Bovey (1973)
Acta Arithmetica
William A. Webb (1976)
Časopis pro pěstování matematiky
Carlo Viola (1973)
Acta Arithmetica
Tripathi, Amitabha (2008)
Integers
Christopher Hooley (1980)
Journal für die reine und angewandte Mathematik
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