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1.
利用同余式、平方剩余、Pell方程的解的性质、递归序列证明了:不定方程x3-1=749y2仅有整数解(x,y)=(1,0). 相似文献
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Muharem Avdispahi 《Mathematische Nachrichten》2019,292(4):691-693
We correct the exponent in the error term of the prime geodesic theorem for hyperbolic 3‐manifolds 1 and in Park's theorem for higher dimensions [ 3 , 2 ]. 相似文献
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Firoz Firozzaman Fahim Firoz 《International Journal of Mathematical Education in Science & Technology》2017,48(5):756-762
Understanding the solution of a problem may require the reader to have background knowledge on the subject. For instance, finding an integer which, when divided by a nonzero integer leaves a remainder; but when divided by another nonzero integer may leave a different remainder. To find a smallest positive integer or a set of integers following the given conditions, one may need to understand the concept of modulo arithmetic in number theory. The Chinese Remainder Theorem is a known method to solve these types of problems using modulo arithmetic. In this paper, an efficient remainder rule has been proposed based on basic mathematical concepts. These core concepts are as follows: basic remainder rules of divisions, linear equation in slope intercept form, arithmetic progression and the use of a graphing calculator. These are easily understood by students who have taken prealgebra or intermediate algebra. 相似文献
6.
Assume a fixed point v∈VG can be separated from zero by a homogeneous invariant f∈𝕜[V]G of degree prd, where p>0 is the characteristic of the ground field 𝕜 and p,d are coprime. We show that then v can also be separated from zero by an invariant of degree pr, which we obtain explicitly from f. It follows that the minimal degree of a homogeneous invariant separating v from zero is a p-power. 相似文献
7.
Shai Sarussi 《代数通讯》2017,45(1):411-419
Let T be a totally ordered set and let D(T) denotes the set of all cuts of T. We prove the existence of a discrete valuation domain Ov such that T is order isomorphic to two special subsets of Spec(Ov). We prove that if A is a ring (not necessarily commutative), whose prime spectrum is totally ordered and satisfies (K2), then there exists a totally ordered set U?Spec(A) such that the prime spectrum of A is order isomorphic to D(U). We also present equivalent conditions for a totally ordered set to be a Dedekind totally ordered set. At the end, we present an algebraic geometry point of view. 相似文献
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For any integer n ≥ 2, let P(n) be the largest prime factor of n. In this paper, we prove that the number of primes p ≤ x with P(p-1) ≥ p~c is more than(1-c + o(1))π(x) for 0 c 1/2. This extends a recent result of Luca, Menares and Madariaga for1/4≤ c ≤1/2. We also pose two conjectures for further research. 相似文献
10.
Graphene is scientifically and commercially important because of its unique molecular structure which is monoatomic in thickness, rigorously two-dimensional and highly conjugated. Consequently, graphene exhibits exceptional electrical, optical, thermal and mechanical properties. Herein, we critically discuss the surface modification of graphene, the specific advantages that graphene-based materials can provide over other materials in sensor research and their related chemical and electrochemical properties. Furthermore, we describe the latest developments in the use of these materials for sensing technology, including chemical sensors and biosensors and their applications in security, environmental safety and diseases detection and diagnosis. 相似文献