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Contents












                        Introduction and Dedication                                   vii




                         I. The Idea of Analytic Number Theory                          1
                           Addition Problems                                            1
                           Change Making                                                2
                           Crazy Dice                                                   5
                           Can r(n) be “constant?”                                      8
                           A Splitting Problem                                          8
                           An Identity of Euler’s                                      11
                           Marks on a Ruler                                            12
                           Dissection into Arithmetic Progressions                     14




                        II. The Partition Function                                     17

                           The Generating Function                                     18
                           The Approximation                                           19
                           Riemann Sums                                                20
                           The Coefficients of q(n)                                     25




                        III. The Erd˝ os–Fuchs Theorem                                 31
                           Erd˝ os–Fuchs Theorem                                       35




                        IV. Sequences without Arithmetic Progressions                  41
                           The Basic Approximation Lemma                               42


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