Trinomial coefficients, Fibonacci numbers and units of the group \(\mathcal{U}(\mathbb{Z} C_p)\) (Q2032742)

The reviewed paper treats the behavior of the trinomial coefficients, Fibonacci numbers and the elements of the group \(U(\mathbb{Z}C_p)\) of units in the integral group ring \(\mathbb{Z}C_p\), where \(C_p\) is a cyclic group of order \(p\) for some fixed prime number \(p\). The main results are the rather technical Theorems 3.1 and 4.1 which describe the coefficients in the expansion of positive integral powers of units of the type \(-1 + g + g^{-1}\) as a lacunary sum of trinomial coefficients, as well as for the particular case \(p=5\) the authors characterize these coefficients in terms of Fibonacci numbers. Some additional explaining examples and remarks are also included in the work.