[obm-l] Problema com inteiros gaussianos

["Jackson Graziano" <jackson@xxxxxxxxx>]

Caros amigos,

Como devo interpretar o enunciado abaixo? Nao consegui entender como são as
regras dele pra andar na reta real...

One cannot walk to infinity on the real line if one uses steps of bounded
length and steps on the prime numbers. This is simply a restatement of the
classic result that there are arbitrarily large gaps in the primes. The
proof is simple: a gap of size k is given by (k + 1)! + 2, (k + 1)! + 3,...,
(k + 1)! + (k,+1).
But the same problem in the complex realm is unsolved. More precisely, an
analogous question asks whether one can walk to infinity in Z[i], the
Gaussian integers, using the Gaussian primes as stepping stones, and taking
steps of bounded length

Obrigado,

Jackson Graziano

=========================================================================
Instruções para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~nicolau/olimp/obm-l.html
O administrador desta lista é <nicolau@mat.puc-rio.br>
=========================================================================