## A selection of problems in the theory of numbers |

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### Contents

ON THE BORDERS OF GEOMETRY AND ARITHMETIC | 7 |

WHAT WE KNOW AND WHAT WE DO NOT KNOW ABOUT PRIME NUMBERS | 25 |

Prime divisors of a natural number | 26 |

24 other sections not shown

### Common terms and phrases

affirmative answer the question arithmetic progressions formed circle with centre circumference composite number cubes of natural D. H. Lehmer decomposition deduce denote different prime numbers divided easy to prove easy to show equation exactly n lattice example exist infinitely exist natural numbers exist prime numbers Fermat numbers finite number G. H. Hardy given natural number Hence infinitely many natural infinitely many prime infinitely many solutions integral coefficients J. E. Littlewood J. W. S. Cassels Lagrange's theorem lattice points least one prime lemma Mersenne numbers natural divisors natural numbers greater number n number of primes numbers Fn obtain obviously odd number odd prime number perfect numbers plane polynomial positive integers prime divisor prime factors quadratic residues rational number rational points Schinzel Sierpinski solutions in prime squares of natural straight line successive natural numbers successive prime numbers sum of three three odd primes twin primes whence Wilson's theorem