Number Theory

Abstract

Letx be a real number. Denote by [x] the integral part of x, i.e. the integer that satisfies the inequalities

$$ \left[ {\text{x}} \right] \underline \leqslant {\text{x}} < \left[ {\text{x}} \right] + {1} $$

We have for example

$$ \left[ \pi \right] = {3},\left[ {2} \right]{ } = {2},\left[ { - 0.{73}} \right] = - {1} $$

.

Number theory is concerned with the integers ..., -3, -2, -1, 0, 1, 2, 3, ... (mainly, although not exclusively, see Chap. 4). Throughout the present Part VIII we shall sometimes omit to mention that a number under consideration is an integer (or, more specifically, a positive or a non-negative integer) if this is sufficiently clear from the context or from the notation; thus n usually denotes an integer.