Parallel p-adic computation (Q1112858)

The author elaborates a multiple p-adic arithmetic which is based on the g-adic expansions of the real numbers. He describes an algorithm for the g-adic expansion of the rational numbers, where \(g=p_ 1p_ 2...p_ k\) is a product of distinct prime numbers. He establishes a one-to-one correspondence between Farey fractions and Hensel codes and obtains a g- version of the Chinese remainder theorem. An improvement of the system is derived from a pipeline architecture with consecutive digits arriving during consecutive cycles. The results of the paper are confered with corresponding multiple-modulus arithmetic. The author discusses the case \(g=2.3.5.7=210\).