[PDF] Mathematical Olympiads 1997-1998: Problems and Solutions from



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Mathematical Olympiads 1997-1998: Problems and Solutions from

nis de ned by a 1 = 1, and a nis the n-th positive integer greater than a n1 which is congruent to nmodulo k Find a nin closed form Solution: We have a n= n(2+(n 1)k)=2 If k= 2, then a n= n2 First, observe that a 1 1 (mod k) Thus, for all n, a n n (mod k), and the rst positive integer greater than a n1 which is congruent to nmodulo kmust



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CHRISTOPHE PETIT

1997 - 2000 Olympiade Math ematique Belge : second prize in 2000, fourth price in 1997 and 1999, nalist in 1998 Olympiade de Physique Belge : nalist in 1999 and 2000 American International Mathematical Examination : ranked sec-ond for Belgium in 2000 2000 Novel contest Victor, organized by le Soir in 2000 : second price Community services



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