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11.
证明了:假设λ,μ是不全为负的非零实数,λ是无理数,k是正整数,那么存在无穷多素数p,p_1,p_2,使得[λp_1+μp_2~2]=kp.特别地,[λp_1+μp_2~2]表示无穷多素数. 相似文献
12.
Under certain condition, the inequality |λ_1p_1~2 λ_2p_2~2 λ_3p_3~2 λ_4p_4~2 μ_12~(x1) … μ_s2~(xs) γ|<ηhas infinitely many solutions in primes p_1,p_2,p_3,p_4 and positive integers x_1,…,x_s. 相似文献
13.
Trevor D. Wooley 《Compositio Mathematica》1998,111(2):149-165
Let p be a rational prime number. We refine Brauer's elementary diagonalisation argument to show that any system of r homogeneous polynomials of degree d, with rational coefficients, possesses a non-trivial p-adic solution provided only that the number of variables in this system exceeds (rd
2)2d-1. This conclusion improves on earlier results of Leep and Schmidt, and of Schmidt. The methods extend to provide analogous conclusions in field extensions of Q, and in purely imaginary extensions of Q. We also discuss lower bounds for the number of variables required to guarantee local solubility. 相似文献
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Ajai Choudhry 《Journal of Number Theory》2005,110(2):317-324
While parametric solutions of the diophantine equation are known for any integral value of s?2, the complete solution in integers is not known for any value of s. In this paper, we obtain the complete solution of this equation when s?13. 相似文献
17.
We define the minimal transversal of a numerical semigroup with respect to one of its elements and use it to calculate the Frobenius number, genus, and the Hilbert function of the semigroup. We give various examples for the use of this method. 相似文献
18.
For a non-decreasing integer sequence a=(a1,...,an) we define La to be the set of n-tuples of integers = (1,...,n) satisfying
. This generalizes the so-called lecture hall partitions corresponding to ai=i and previously studied by the authors and by Andrews. We find sequences a such that the weight generating function for these a-lecture hall partitions has the remarkable form
In the limit when n tends to infinity, we obtain a family of identities of the kind the number of partitions of an integer m such that the quotient between consecutive parts is greater than is equal to the number of partitions of m into parts belonging to the set P, for certain real numbers and integer sets P. We then underline the connection between lecture hall partitions and Ehrhart theory and discuss some reciprocity results. 相似文献
19.
本文对不定方程x2+y2=z2给出了四个推广,并用一种统一的解法对这四个推广给出了解答. 相似文献
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