A note on the polynomial-exponential Diophantine equation (a(n) - 1) (b(n) - 1) = x(2)

期刊： NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2021; 27 (3)

For any positive integer t, let ord(2) t denote the order of 2 in the factorization of t. Let a, b be two distinct fixed positive integers with min{a,......

On the Diophantine equations z(2) = f(x)(2) +/- f(x) f(y)

期刊： NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2021; 27 (2)

Using the theory of Pell equation, we study the non-trivial positive integer solutions of the Diophantine equations z(2) = f(x)(2) +/- f(x) f(y) + f(y......

The character sum of polynomials with k variables and two-term exponential sums

期刊： NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2021; 27 (1)

The main purpose of this paper is using the properties of the classical Gauss sums and the analytic methods to study the computational problem of one ......

On a class of quartic Diophantine equations

期刊： NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2021; 27 (1)

In this paper, by using elliptic curves theory, we study the quartic Diophantine equation (DE) Sigma(n)(i=1) a(i)x(i)(4) = Sigma(n)(j=1) a(j)y(j)(4), ......

A Diophantine equation about polygonal numbers

期刊： NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2021; 27 (3)

It is well known that the number P-k (x) = x((k - 2)(x - 1) + 2/2 is called the x-th k-gonal number, where x >= 1, k >= 3. Many Diophantine equa......