Sentence examples for elementary methods to from inspiring English sources

Like other successful attacks, Hacker Croll used the same combination of patience, sheer determination and somewhat elementary methods to gain access to a frightening number of accounts and services related to Twitter and Twitter employees.

In this paper, we employ elementary methods to investigate the reciprocal sums of the products of two Fibonacci numbers in several ways.

Most of them, both in 2D and 3D, share a common approach, using numerical data to manage geometric knowledge and elementary methods to compute derived objects.

In this paper, we study the properties of Chebyshev polynomials of the first and second kind and those of Fibonacci polynomials and use an elementary method to give Chebyshev polynomials of the first and second kind in terms of Fibonacci polynomials and vice versa.

Elementary methods suffice to prove the inequalities.

In this paper, we use the properties of Chebyshev polynomials, elementary methods, and combinational techniques to study the computational problem of one kind of convolution sums involving second kind Chebyshev polynomials, and we give an exact computational method, which expresses the sums as second kind Chebyshev polynomials.

This does not mean that he restricts himself to just elementary methods; he does use stronger tools but it is crucial that they apply uniformly to all real closed fields.

In this paper, we shall use the elementary methods and estimate for character sums to study this problem, and prove the following conclusion.

In this paper, we shall use the elementary and combination methods to study the arithmetical properties of Lucas polynomials, and give some new identities for them.

The main purpose of this paper is, using the elementary and combination methods, to study the arithmetical properties of the Lucas polynomials and to obtain some new and interesting identities for them.

In this paper, we introduce a new sum, analogous to Cochrane sums, and use elementary and analytic methods to study the hybrid mean value problem involving this sum and Kloosterman sums, and we give an interesting asymptotic formula for it.