Hello,
Here is what I was able to come up with. gap> n:=12;;Filtered(Cartesian([1..n],[2..n]),v->((2^v[1]-1) mod v[2])=0); [ [ 2, 3 ], [ 3, 7 ], [ 4, 3 ], [ 4, 5 ], [ 6, 3 ], [ 6, 7 ], [ 6, 9 ], [ 8, 3 ], [ 8, 5 ], [ 9, 7 ], [ 10, 3 ], [ 10, 11 ], [ 12, 3 ], [ 12, 5 ], [ 12, 7 ], [ 12, 9 ] ] Basically, one iterates over ordered pairs in [1..n] x [2..n] where 'b' is the first coordinate 'v[1]' and 'a' is the second 'v[2]'. The [2..n] being the second coordinate is to omit the trivial case of 1 dividing 2^b-1. I make no claims that this is the most efficient solution. I hope this helps. -Tim Kohl On Thu, 21 Jan 2021, lopo apelo kosho wrote: > Dear Friends, > I am searching for non-negative integers a and b in an interval [0,n] such > that a divides (2^b-1). > It is supposed to have a-any odd number and b=phi(a). I tried to find those > values using GAP (please see below) but it seems that I am doing mistake. > fun:=function(n) local a,b,t; > t:=[]; > for a in [1..n] do; > for b in [1..n ] do; > if 2^b-1 = 0 mod a > then Add (t,(a,b)); > fi; > return t; > od; > od; > end; > > > I will be thankful for any help:. > Regards > > _______________________________________________ > Forum mailing list > Forum@gap-system.org > https://mail.gap-system.org/mailman/listinfo/forum > _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
