xii PREFAC E
use computer s an d softwar e t o d o mathematics , ou r boo k ca n certainl y hel p the m
in thi s task . Indeed , man y o f th e problem s encourag e th e reade r t o us e compute r
software an d a t times , whil e searchin g fo r a solution , indicat e ho w t o writ e th e
program tha t wil l bring abou t th e solutio n t o th e problem .
Although mos t problem s presente d her e us e basi c result s whic h ca n b e foun d
in just abou t an y elementary boo k i n number theory , w e chose to includ e a sectio n
which provides the basic definitions an d the main theorems one needs to handle th e
various subject s covered i n th e book . Thi s "too l box " ha s th e advantag e tha t th e
reader doe s not hav e to search her e an d ther e fo r th e basi c notions neede d t o solv e
the problems . Finally , we found i t convenien t t o includ e i n this section a list o f th e
main arithmeti c function s wit h thei r definitions , a s wel l a s a lis t o f th e constant s
and symbol s mos t frequentl y use d i n the text .
Our presentatio n i s as follows : th e first sectio n provide s th e basi c theor y rele -
vant fo r th e understandin g an d th e resolutio n o f th e state d problems ; th e secon d
section gather s th e statement s o f the problems ; while the thir d sectio n list s al l th e
solutions. A t the end of the book, th e reader wil l find a bibliography, a terminolog y
index an d a n inde x o f authors .
We want t o thank al l those who, by their remark s an d suggestions , contribute d
to th e realizatio n o f this manuscript . I n particular , ou r thank s g o to Jean-Lo u D e
Carufel (Quebec) , Nicola s Doyo n (Quebec) , Davi d Gil l (Quebec) , Jacque s Gra h
(Quebec), Nicola s Gua y (Quebec) , Aleksanda r Ivi c (Belgrade) , Imr e Kata i (Bu -
dapest), Claud e Levesque (Quebec) , Marc-Hubert Nicol e (Quebec) , Erik Pronovos t
(Quebec) an d Gu y Robi n (Limoges) .
Part o f thi s wor k wa s don e i n 200 3 an d 200 4 whil e th e first autho r wa s o n
sabbatical i n Tucson, Arizona . Thi s autho r i s grateful t o the Departmen t o f Math -
ematics of the University of Arizona, i n particular t o Professor Willia m Yslas Velez,
for makin g thi s possible .
Jean-Marie D e Koninc k
Armel Mercie r
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