Prime numbers, friends who give problems. A trialogue with Papa Paulo
The present book by Paulo Ribenboim is an introduction to those parts of elementary number theory that are also discussed extensively in his other books: prime numbers, congruences, Lucas sequences, primality tests. The idea is to explain the contents as clearly as possible, but without proofs except those that are sufficiently simple. The whole book is written as a ``trialogue'' between ``Papa Paulo'' and two boys named Paulo and Eric. Every now and then there are historical interludes, with occasional slips: the binomial theorem for positive integral exponents, for example, is credited to Newton. More seriously, the following sentences on p. 212 are all incorrect: Euler ``was able to prove that for every \(s > 1\) the series \(\sum_{n=1}^\infty \frac1{n^s}\) is convergent. He did not try to compute explicitly the sum of the series, except when \(s\) is an even integer and \(s \geq 2\) [\dots]. But he gave a name to the sum: \(\zeta(s)\)''.NEWLINENEWLINEThe last pages of the book explain, in Ribenboim's words, the reasons why Springer-Verlag New York turned down the manuscript: because it is funny and it ``explains everything about prime numbers in a language without secrets'', whereas Springer's aim is selling books that ``generate confusion''. If this is your kind of humor, then this book is for you.
scientific article; zbMATH DE number 6656296