Titlebook: Number Theory in Science and Communication; With Applications in Manfred R. Schroeder Book 19841st edition Springer-Verlag Berlin Heidelber

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Primesds counter-intuitive and, in fact, it isn’t true, as Euclid demonstrated a long time ago. Actually, he did it without demonstrating any primes — he just showed that assuming a finite number of primes leads to a neat contradiction.

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Quadratic Congruencesnication tasks as certified receipts, remote signing of contracts, and coin tossing — or playing poker over the telephone (discussed in Chap. 19). Finally, quadratic congruences are needed in the definition of pseudoprimes, which were once almost as important as actual primes in digital encryption (see Chap. 19).

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IntroductionHermann Minkowski, being more modest than Kronecker, once said “The primary source (Urquell) of all of mathematics are the integers.” Today, integer arithmetic is important in a wide spectrum of human activities and natural phenomena amenable to mathematic analysis.

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The Natural NumbersHere we encounter such basic concepts as ., ., and ., and we learn the very fundamental fact that the composites can be represented in a . way as a product of primes.

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Knapsack EncryptionAs a diversion we return in this chapter to another (once) promising public-key encryption scheme using a trap-door function: . It, too, is based on residue arithmetic, but uses multiplication rather than exponentiation, making it easier to instrument and theoretically more transparent.