to Chebyshev
0. Introduction
To count is in the first place to count on oneself. In a figurative sen
of course, but also in the ordinary sense: to count on one's finge
on one's toes, on one's shoulders, on one's knees, e£c.Etymology
names of numbers indeed reveals remnants of very ancient langua
in which they denoted the different parts of the body. As archety
of our representation of the world, numbers form, in the strong
sense, part of ourselves, to such an extent that it can legitimately
asked whether the subject of study of arithmetic is not the hum
mind itself. Prom this a strange fascination arises: how can it
that these numbers, which lie so deeply within ourselves, also g
rise to such formidable enigmas? Among all these mysteries, that
the prime numbers is undoubtedly one of the most ancient and m
resistant. What we aim at in this book is to initiate the reader i
some of the methods invented by man to apprehend this far fr
compliant intimacy. May he gauge the extent of our ignorance us
these interrelated mysteries as a measure and develop from that
insatiable thirst for understanding.
There are, fundamentally, two ways of combining integers. Th
can be added and they can be multiplied together. Yet although,
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