## Biscuits of Number TheoryIn Biscuits of Number Theory, the editors have chosen articles that are exceptionally well-written and that can be appreciated by anyone who has taken (or is taking) a first course in number theory. This book could be used as a textbook supplement for a number theory course, especially one that requires students to write papers or do outside reading. The editors give examples of some of the possibilities. The collection is divided into seven chapters: Arithmetic, Primes, Irrationality, Sums of Squares and Polygonal Numbers, Fibonacci Numbers, Number Theoretic Functions, and Elliptic Curves, Cubes and Fermat's Last Theorem. As with any anthology, you don't have to read the Biscuits in order. Dip into them anywhere: pick something from the Table of Contents that strikes your fancy, and have at it. If the end of an article leaves you wondering what happens next, then by all means dive in and do some research. You just might discover something new! |

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### Contents

I | 1 |

II | 3 |

III | 13 |

IV | 17 |

V | 23 |

VI | 39 |

VII | 53 |

VIII | 59 |

XXVI | 143 |

XXVII | 145 |

XXVIII | 147 |

XXIX | 149 |

XXX | 153 |

XXXI | 155 |

XXXII | 157 |

XXXIII | 167 |

IX | 61 |

X | 63 |

XI | 65 |

XII | 67 |

XIII | 69 |

XIV | 77 |

XV | 85 |

XVI | 105 |

XVII | 107 |

XVIII | 109 |

XIX | 111 |

XX | 113 |

XXI | 115 |

XXII | 121 |

XXIII | 129 |

XXIV | 133 |

XXV | 141 |

XXXIV | 183 |

XXXV | 195 |

XXXVI | 199 |

XXXVII | 217 |

XXXVIII | 223 |

XXXIX | 225 |

XL | 233 |

XLI | 251 |

XLII | 255 |

XLIII | 257 |

XLIV | 259 |

XLV | 269 |

XLVI | 273 |

XLVII | 285 |

XLVIII | 287 |

### Common terms and phrases

algebraic algorithm Amer arithmetic balanced prime base binomial coefficients cell coefficients colored combinatorial complex compute congruent number conjecture Conrey consecutive consider continued fraction cubes define denominators denote digits divides domino elementary elliptic curves Erdos Euler example exist exponent fact factorial function Fermat's Last Theorem Fibonacci and Lucas Fibonacci numbers field sieve Figure finite formula Galois greatest common divisor Hence infinitely irrational number lattice points Lemma Lucas numbers Math mathematicians method modular form modulo multiple natural numbers nonzero number field sieve number theory Originally appeared p-adic p-ordering paper polynomial positive integer prime factor prime numbers problem proof properties prove pseudoperfect Pythagorean triples quadratic sieve question random matrix theory rational numbers reduced relatively prime representation result Riemann Hypothesis Riemann zeta function right triangle satisfying sequence of remainders solutions square subset symmetric values visual weird numbers Wiles world champions zeros