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1.
证明了:如果λ1,…,λ11,μ是非零实数,并且不同一符号,至少有一个λi/λj是无理数,那么对任意实数η和ε>0,不等式λ1x14 … λ11x141 μy2 η<ε有无穷多正整数解x1,…,x11,y. 相似文献
2.
Hong Ze Li 《数学学报(英文版)》2001,17(1):153-160
Let λ1, λ2,..., λ7 be real numbers satisfying λ
i
≥ 1. In this paper, we prove there are integers x
1,..., x
7 such that the inequalities |λ1
x
3
1 + λ2
x
3
2 + ⋯ + λ7
x
3
7| < 1 and hold simultaneously.
Received November 18, 1997, Accepted October 23, 1998 相似文献
3.
In this paper,it is shown that:if λ1,..,λ8 are nonzero real numbers,not all of the same sign,such that λ1/λ2 is irrational,then for any real numbex,η and ε>0 the inequality,|λ1x21 λ2x22 λ3x43 … λ8x48 η|<ε has infinitely many solutions in positive integers x1,…,x8. 相似文献
4.
本文证明了如果λ1,…,λ6是非零实数,并且不同一符号,至少有一个λi/λj(1≤i,j≤3)是无理数,那么对任意实数η和ε>0,不等式|λ1x21+λ2x22+λ3x23+λ4x44+λ5x45+λ6x46+η|<ε有无穷多正整数解x1,…,x6. 相似文献
5.
朱立 《数学年刊A辑(中文版)》2019,40(4):365-376
令■设λ_1,λ_2,λ_3是不全同号的非零实数,且满足λ_1/λ_2为无理数,则对于任意实数η和ε 0,不等式■有无穷多组素数解p_1,p_2,p_3.该结果改进了Gambini,Languasco和Zaccagnini的结果. 相似文献
6.
7.
8.
This paper proves conditional existence results for non-trivialsolutions of the equation where the coefficients ai and the unknowns Xi are taken to berational integers. No such results were previously known for n6. The proofs useelementary facts about the 3-descent procedure for ellipticcurves of the form EA: X3 + Y3 = AZ3. Thus, when n=4, and the ai are each prime, and are all congruentto 2 modulo 3, it is shown that (*) will have non-trivial solutions,providing that the Selmer conjecture holds for the curves EA.One may replace the Selmer conjecture by an appropriate formof the Generalized Riemann Hypothesis, when n=5 and the ai areagain taken to be primes, all congruent to 8 modulo 9. Finally,when n=5, one may require only that the ai be square-free andcoprime to 3, providing one assumes both the Selmer conjectureand a special case of Schinzel's conjecture (on the representationof primes by cubic polynomials). 1991 Mathematics Subject Classification:11D25, 11G05, 14G05. 相似文献
9.
一个素变数丢番图不等式 总被引:1,自引:0,他引:1
本文证明了如果1<c<237/214,则对于充分大的N和ε≥N-1/5(237/214-c)+v(v>0)表达式D(N):=Σ|pc1+pc2+pc3-N|<-εlogp1logp2logp3 关于素变数p1,p2,p3有渐近公式,改进了文献[1]的结果1<C<1.1. 相似文献
10.
11.
We generalize Chebotarev’s density theorem to Weil groups. Since the Artin–Weil conjecture on the integrality of the Artin–Hecke L-functions, constructed by A. Weil, has not been completely proved so far, we estimate the character sums both under and without the assumption of the validity of that conjecture. 相似文献
12.
Pr表示最多r个素因子的正整数.作者证明了,对于任一足够大的实数N和1<c<c0,不等式|pc+Pcr-N|<N9/10(1-c0/c)对素数p和Pr是可解的.特别地,当1<c<c0=1.03074432…,有r=6.这个结果改进了翟文广和曹晓东的结果. 相似文献
13.
一个素变数的Diophantine不等式 总被引:3,自引:3,他引:0
设1<C<13/12.本文证明了存在N(C)>0使得对任意实数N>N(C),下面的不等式|++ -N|<N- )logsN有素数解p1,p2,p3,其中s=2(15). 相似文献
14.
令.本文证明了存在N(c)>0,对任意实数N>N(c),不等式有素数解p1,p2,p3,其中c1为一绝对正常数. 相似文献
15.
16.
By using a more efficient way of almost diagonalizing,known results on small fractional parts of general real cubicforms in a small number of variables, are improved. In particular,for ternary forms the method gives a bound superior to thatarising from simply reducing to a cubic form in one variable.2000 Mathematics Subject Classification 11D75, 11E76, 11J54. 相似文献
17.
On a Binary Diophantine Inequality Involving Prime Numbers 总被引:1,自引:0,他引:1
M. B. S. Laporta 《Acta Mathematica Hungarica》1999,83(3):179-187
Let 1 < c < 15/14 and N a sufficiently large real number. In this paper we prove that, for all (N, 2N\ A with
, the inequality
has solutions in primes
. 相似文献
18.
Integer Solutions are found to the equations t23(a2,b2, (a + b)2, (ab)2) = p2, q2, r2, s2. These lead surprisinglyto solutions to the equations u2 + (c2, d2, (c + d)2, (c d)2) = p2, q2, v2, w2, with the same values of p and q. 相似文献
19.
In this short note we prove that if 1 < c < 81/40, c ≠ 2, N is a large real number, then the Diophantine inequality
is solvable, where p
1,···,p
5 are primes. 相似文献
20.
证明了:设k是大于或等于2的正整数,η是任意给定的实数,λ_1,λ_2,λ_3是非零实数,不全同号,并且λ_1/λ_2是无理数,则不等式|λ_1p_1+λ_2p_2+λ_3p_32~k+η|(max p_j)~(-σ)有无穷多组素数解p_1,p_2,p_3,这里σ满足:当2≤k≤3时,0σ1/2(2~(k+1)+1),当4≤k≤5时,0σ5/6k2~k;当k≥6时,0σ20/21k2~k. 相似文献