Unsolved problems in number theory
Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane 's Online Encyclopedia of Integer Sequences, at the end of several of the sections.
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A Prime Numbers
A5 Arithmetic progressions of primes 15 A6 Consecutive primes
A16 Gaussian primes EisensteinJacobi primes 33 A17 Formulas
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Acta Arith algorithm aliquot sequences amicable numbers amicable pairs arithmetic progressions binomial coefficients Bull Canad Carl Pomerance Carmichael numbers Colloq Comput Conf congruences consecutive integers consecutive primes covering systems cuboid D. H. Lehmer Davenport-Schinzel sequences density diophantine equation Discrete Math distinct prime divisors Egyptian fractions Elem Erdos asks Euler's example Fermat numbers Fibonacci Fibonacci Quart function graph Heath-Brown hyperperfect infinitely integers J. L. Selfridge lattice points least prime Leo Moser London Math lower bound Makowski Math Mersenne primes modulo Monthly nombres notes number of primes number of solutions Number Theory partition Paul Erdos positive integers powerful numbers prime factors prime numbers Proc proof proved pseudoprimes quadratic residue R. L. Graham rational Recreational Math reine angew Richard Schinzel sets of integers showed shown Sierpiriski smallest squarefree squares Straus subset theorem triangle Uber unitary perfect Univ values