MathDB
Miklos Schweitzer 1977_3

Source: p-adic

January 25, 2009
logarithmssuperior algebrasuperior algebra unsolved

Problem Statement

Prove that if a,x,y a,x,y are p p-adic integers different from 0 0 and px,paxy p | x, pa | xy, then \frac 1y \frac{(1\plus{}x)^y\minus{}1}{x} \equiv \frac{\log (1\plus{}x)}{x} \;\;\;\; ( \textrm{mod} \; a\ ) \\\\ . L. Redei