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(Solved): The n-th Galois number is defined by G_(n)=\sum_(j=0)^n [[n],[j]]_(q) Show that Galois numbers satis ...
The n-th Galois number is defined by
G_(n)=\sum_(j=0)^n [[n],[j]]_(q)
Show that Galois numbers satisfy the following recursive relation
G_(n+1)=2G_(n)+(q^(n)-1)G_(n-1)
with G_(0)=1 and G_(1)=2. Find the limit: \lim_(q->1)G_(n).