Geometric configurations in the ring of integers modulo p^{ell}

M ay 2 01 1 Geometric configurations in the ring of integers modulo pl

We study variants of the Erd˝ os distance problem and the dot products problem in the setting of the integers modulo q, where q = p is a power of an odd prime.

The Ring of Integers, Euclidean Rings and Modulo Integers

The binary operation multint on Z is defined as follows: (Def. 1) For all elements a, b of Z holds (multint)(a, b) = ·R(a, b). The unary operation compint on Z is defined as follows: (Def. 2) For every element a of Z holds (compint)(a) = −R(a). The double loop structure INT.Ring is defined by: (Def. 3) INT.Ring = 〈Z, +Z,multint, 1(∈ Z), 0(∈ Z)〉. Let us mention that INT.Ring is strict and non em...

On transitive polynomials modulo integers

A polynomial P (x) with integer coefficients is said to be transitive modulo m, if for every x, y ∈ Z there exists k ≥ 0 such that P (x) = y (mod m). In this paper, we construct new examples of transitive polynomials modulo prime powers and partially describe cubic and quartic transitive polynomials. We also study the orbit structure of affine maps modulo prime powers.

Arithmetical Definitions in the Ring of Integers

the effect of the record infancy in crimilly acts of guilties (in karaj city)

چکیده یکی از مهمترین دغدغه های بزرگ جوامع بشری، از دیر باز تا کنون که ذهن پژوهشگران و متخصصان بهداشت روانی و اجتماعی و دولتها رابه خود مشغول داشته، مسأله ی بزهکاری می باشد. شناخت کامل پدیده ی بزهکاری و بزهکار، علل وعوامل سقوط یک انسان، چگونگی درمان وی و درنهایت پیشگیری ازبزهکاری ودریک کلام سالم سازی یک جامعه، رسالت عظیم، انسانی ومقدسی می باشد که با بررسی شخصیت مجرم یعنی[ انسانی که تحت شرای...