An ideal Waring problem with restricted summands
نویسندگان
چکیده
منابع مشابه
Compositions with Pairwise Relatively Prime Summands within a Restricted Setting
The paper studies the counting function R2(n, k) = ∑ a1+a2+···+ak=n (ai,aj)=1 i 6=j 1, ai ≥ 1, k ≥ 2 with ai, n and k positive integers and establishes a relationship between R2(n, k) and P2(n, k) where P2(n, k) = ∑ a1+a2+···+ak=n 1≤a1≤a2≤···≤ak≤n (ai,aj)=1 i 6=j 1, ai ≥ 1, k ≥ 2 with ai, n, k positive integers. 1. PRELIMINARIES Gould [4], studied the number-theoretic function R(n, k) = ∑ a1+a2...
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It is conjectured that Lagrange’s theorem of four squares is true for prime variables, i.e. all positive integers n with n 4 ðmod 24Þ are the sum of four squares of primes. In this paper, the size for the exceptional set in the above conjecture is reduced to OðN 3 8 þeÞ: r 2004 Elsevier Inc. All rights reserved. MSC: 11P32; 11P05; 11N36; 11P55
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1994
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-66-2-125-132