# Unsolved Problems in Number Theory

Springer Science & Business Media, Mar 9, 2013 - Mathematics - 438 pages

Mathematics is kept alive by the appearance of new unsolved problems, problems posed from within mathematics itself, and also from the increasing number of disciplines where mathematics is applied. This book provides a steady supply of easily understood, if not easily solved, problems which can be considered in varying depths by mathematicians at all levels of mathematical maturity.

For this new edition, the author has included new problems on symmetric and asymmetric primes, sums of higher powers, Diophantine m-tuples, and Conway's RATS and palindromes. The author has also included a useful new feature at the end of several of the sections: lists of references to OEIS, Neil Sloane's Online Encyclopedia of Integer Sequences.

"...many talented young mathematicians will write their first papers starting out from problems found in this book." András Sárközi, MathSciNet

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### Contents

 Introduction 1 Primes of shape k 2 + 1 13 A4 The prime number race 22 A5 Arithmetic progressions of primes 25 A6 Consecutive primes 43 A16 Gaussian and EisensteinJacobi primes 55 A17 Formulas 66 B3 Unitary perfect numbers 84 B4 Amicable 91 B11 Solutions of mom no n 101 B12 Analogs with dn 105 B17 Exponentialperfect numbers 110 B18 Solutions 124 B33 Largest divisor of a binomial coefficient 134 B34 If theres an i 138
 Diophantine Equations 209 D1 Sums of like powers Eulers conjecture 209 D2 The Fermat 237 D10 Exponential diophantine equations 242 D11 Egyptian 275 D20 Six general points at rational distances 287 D21 Triangles with 301 E4 Sequence with no member dividing the product of r others 314 E13 Partitioning into strongly sumfree classes 327 E14 Rados 330 with A P S 345 E24 Irrationality sequences 346 E25 Golombs 353 F1 Gaußs lattice point problem 365 F2 Lattice points with distinct 377

 B42 Behavior of pan and a pn 150 B43 Alternating sums 154 C3 Lucky numbers 164 C4 Ulam numbers 166 C5 Sums 175 C11 Threesubsets with distinct sums 184 C12 The postage stamp 190 C18 The n queens problem 200 C19 Is a weakly indedendent 207
 F13 Covering systems of congruences 383 F14 Exact 390 F28 A determinant of value one 401 F29 Two congruences one 403 General Index 429 Copyright