Quadratic forms representing all integers coprime to 3
نویسندگان
چکیده
منابع مشابه
Quadratic Forms Representing All Odd Positive Integers
We consider the problem of classifying all positive-definite integer-valued quadratic forms that represent all positive odd integers. Kaplansky considered this problem for ternary forms, giving a list of 23 candidates, and proving that 19 of those represent all positive odds. (Jagy later dealt with a 20th candidate.) Assuming that the remaining three forms represent all positive odds, we prove ...
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The asymptotic behaviour of the sequence with general term $P_n=(varphi(1)+varphi(2)+cdots+varphi(n))/(1+2+cdots+n)$, is studied which appears in the studying of coprime integers, and an explicit bound for the difference $P_n-6/pi^2$ is found.
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d|en d denote the number and the sum of exponential divisors of n, respectively. Properties of these functions were investigated by several authors, see [1], [2], [3], [5], [6], [8]. Two integers n,m > 1 have common exponential divisors iff they have the same prime factors and for n = ∏r i=1 p ai i , m = ∏r i=1 p bi i , ai, bi ≥ 1 (1 ≤ i ≤ r), the greatest common exponential divisor of n and m is
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There are 65 known positive integers n for which a prime number p prime to D is of the form x2 + ny2 iff p lies in certain congruence classes modulo 4n: these are the idoneal numbers. (It is known that there is at most one further such number and if such a 66th idoneal number exists, then the Generalized Riemann Hypothesis is false.) For n = 1 this is Fermat’s Two Squares Theorem: an odd prime ...
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2017
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-016-9883-0