منابع مشابه
Sums of almost equal prime squares
In this short note, we prove that almost all integers N satisfying N ≡ 3 (mod 24) and 5 -N or N ≡ 4 (mod 24) is the sum of three or four almost equal prime squares, respectively: N = p21 + · · ·+ p 2 j with |pi − (N/j) 1/2| ≤ N1/2−9/80+ε for j = 3 or 4 and 1 ≤ i ≤ j.
متن کاملOn Sums of Powers of Almost Equal Primes
We investigate the Waring-Goldbach problem of representing a positive integer n as the sum of s kth powers of almost equal prime numbers. Define sk = 2k(k − 1) when k > 3, and put s2 = 6. In addition, put θ2 = 19 24 , θ3 = 4 5 and θk = 5 6 (k > 4). Suppose that n satisfies the necessary congruence conditions, and put X = (n/s). We show that whenever s > sk and ε > 0, and n is sufficiently large...
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In 1997 K. Ono and K. Soundararajan [Invent. Math. 130(1997)] proved that under the generalized Riemann hypothesis any positive odd integer greater than 2719 can be represented by the famous Ramanujan form x2 + y2+10z2; equivalently the form 2x+5y+4Tz represents all integers greater than 1359, where Tz denotes the triangular number z(z+1)/2. Given positive integers a, b, c we employ modular for...
متن کاملOn generalisations of almost prime and weakly prime ideals
Let $R$ be a commutative ring with identity. A proper ideal $P$ of $R$ is a $(n-1,n)$-$Phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin R$, $a_1cdots a_nin Pbackslash P^m$ ($a_1cdots a_nin Pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin P$, for some $iin{1,ldots,n}$; ($m,ngeq 2$). In this paper several results concerning $(n-1,n)$-$Phi_m$-prime and $(n-1,n)$-...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1996
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-77-4-369-383