Results 171 to 180 of about 288 (212)
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Counting Sums of Three Squares
Bulletin of the London Mathematical Society, 1988Let Q(x) denote the number of positive integers \(n\leq x\) which are sums of three squares, and let \(\Delta\) (x) be defined by \(Q(x)=5x/6+\Delta (x)\). \textit{E. Landau} [Arch. Math. Phys. 13, 303-312 (1908)] proved that \(\Delta (x)\ll \log x\) as \(x\to \infty\). \textit{N. C. Chakrabarti} [Bull. Calcutta Math. Soc.
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Generalising ‘Sums of cubes equal to squares of sums’
The Mathematical Gazette, 2001David Pagni drew attention to a result which is ascribed by Dickson [2, p. 286] to Liouville (1857), that the sum of the cubes of the number of divisors of each of the divisors of an integer, is equal to the square of their sum. For example, the divisors of 6 are 1, 2, 3, and 6,
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Sums Of Squares And Gauss Sums
1995Abstract The concepts introduced so far form the basis for the major topics to be discussed in this chapter, they are Gauss sums and, to begin with, the representation of integers as sums of squares. Consider the proposition: if p is a prime and p = 1 (mod 4), then the Diophantine equation has an integer solution. This result.
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Introducing SummerTime: A package for high-precision computation of sums appearing in DRA method
Computer Physics Communications, 2016Roman N Lee, Kirill T Mingulov
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