The distribution of patterns of inverses modulo a prime

On the Distribution of Inverses Modulo n

On Newton-Raphson iteration for multiplicative inverses modulo prime powers

We study algorithms for the fast computation of modular inverses. Newton-Raphson iteration over p-adic numbers gives a recurrence relation computing modular inverse modulo p, that is logarithmic in m. We solve the recurrence to obtain an explicit formula for the inverse. Then we study different implementation variants of this iteration and show that our explicit formula is interesting for small...

Distribution of Difference between Inverses of Consecutive Integers modulo P

Let p > 2 be a prime number. For each integer 0 < n < p, define n by the congruence nn ≡ 1 (mod p) with 0 < n < p. We are led to study the distribution behavior of n− n+ 1 in order to prove the asymptotic formula p−2 ∑ n=1 |n− n+ 1| = 1 3 p +O(p log p).

the effect of consciousness raising (c-r) on the reduction of translational errors: a case study

در دوره های آموزش ترجمه استادان بیشتر سعی دارند دانشجویان را با انواع متون آشنا سازند، درحالی که کمتر به خطاهای مکرر آنان در متن ترجمه شده می پردازند. اهمیت تحقیق حاضر مبنی بر ارتکاب مکرر خطاهای ترجمانی حتی بعد از گذراندن دوره های تخصصی ترجمه از سوی دانشجویان است. هدف از آن تاکید بر خطاهای رایج میان دانشجویان مترجمی و کاهش این خطاها با افزایش آگاهی و هوشیاری دانشجویان از بروز آنها است.از آنجا ک...

Distribution of Special Sequences modulo a Large Prime

As it was indicated in [5], A. Odlyzko asks for which values of N the set A contains all residue classes (modp). The conjecture is that one can take N to be as small as p1/2+ε, for any positive ε and p > c with some c = c(ε). From the result of Rudnick and Zaharescu [4] it follows that in Odlyzko’s problem one can take N = c0p logp for some absolute constant c0. One of the main results of [5] i...