Problems in Elementary Number Theory

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Problems in Elementary Number TheoryCompiled by Hojoo LeeVersion , Last revised on May, 2003Typeset by LATEXThis book is available at nonprofit use onlyCopyrightc 2003 Hojoo LeeContents1. Introduction12. Divisibility Theory2Problems2Sources53. Congruences6Problems6Sources74. Primes and Composite Numbers7Problems7Sources85. Diophantine Equations8Problems8Sources116. Functions in Number Theory12Problems12Sources147. Rational and Irrational Numbers14Problems14Sources158. Additive Number Theory16Problems16Sources179. Sequences of Integers18Problems18Sources2010. Combinatorial Number Theory21Problems21Sources2311. Miscellaneous Problems23Problems23Sources25PROBLEMS IN Elementary Number THEORYVersion : May heart of Mathematics is its of This BookThe purpose of this book is to present a collection of interesting questions inElementary Number Theory .

PROBLEMS IN ELEMENTARY NUMBER THEORY 3 13. Determine all pairs (n;p) of nonnegative integers such that – p is a prime, – n not exceeded 2p, and – (p¡1)n +1 is divisible by np¡1. 14. Let m and n be natural numbers such that

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