Arithmetic identities involving Bernoulli and Euler numbers (Q5902195)

Through the trigonometric generating functions, the Bernoulli numbers and Euler numbers are defined, respectively, as follows \[ \begin{aligned} x\cot x =&\sum_{n=0}^{\infty}(-1)^n\frac{(2x)^{2n}}{(2n)!}B_{2n}, \quad |x|< 2\pi, \\ \sec x =&\sum_{n=0}^{\infty}(-1)^n\frac{x^{2n}}{(2n)!}E_{2n}, \quad |x|<\frac{\pi}{2}.\end{aligned} \] This paper establishes several classes of arithmetic identities involving the Bernoulli and Euler numbers, by applying the formal power series method to elementary trigonometric sums.