Solving an exponential Diophantine equation
Solving some functional and operational equations.
Some applications of Franel-Kluyver's integral. II.
Some applications of linear forms in logarithms
Some applications of linear forms in logarithms
Some Applications of Sieve Methods in Algebra Number Fields.
Some Arithmetic Properties of the OLIVIER Functions.
Some Arithmetic Sums Connected With the Greatest Integer Function.
Some binary representations of real numbers and odd solutions of the functional equation ... .
Some characterizations of specially multiplicative functions.
Some characterizations of totients.
Some congruence properties of binomial coefficients and linear second order recurrences.
Some congruences for binomial coefficients
Some congruences involving binomial coefficients
Binomial coefficients and central trinomial coefficients play important roles in combinatorics. Let p > 3 be a prime. We show that , where the central trinomial coefficient Tₙ is the constant term in the expansion of . We also prove three congruences modulo p³ conjectured by Sun, one of which is . In addition, we get some new combinatorial identities.
Some divisibility properties of binomial coefficients and the converse of Wolstenholme's theorem.
Some euclidean properties for real quadratic fields
Some further results concerning (j,ε) -normality in the rationals
Some generalizations of the Sₙ sequence of Shanks
Some hypergeometric congruences
Some identities for factorials and binomial coefficients