ACTA issues

A remarkable class of congruences

Peter Bundschuh, Chun-Gang Ji, Zun Shan

Acta Sci. Math. (Szeged) 67:3-4(2001), 493-500

Abstract. In this paper, we deduce from one common source a class of congruences modulo odd primes $p$ most of which are new, e.g. $$\eqalign{\sum_{k=1}^{[p/6]}{ {(-1)^k}\over k} &\equiv\sum_{k=1}^{(p-1)/2}{{3^k}\over k} ({\rm{mod}} p),\cr\sum_{k=1}^{[p/8]}{1\over k} &\equiv{5\over2}\sum_{k=1}^{(p-1)/2}{1\over k}+\sum_{k=1}^{(p-1)/2}{1\over{k\cdot2^k}} ({\rm{mod}} p).}$$

AMS Subject Classification (1991): 11A07, 11A41

Received May 22, 2000. (Registered under 2798/2009.)