(* check for the El'adl part1 *)
(* Attention this theorem is accuracy (acc)
dependent, if you give smaller than
necessary accuracy , it will give WRONG
results *)
acc:=1000
(* we should give enough accuracy (acc), in order to
compute the rationalize[sol1] term *)
m=3 ; (* Attention ! m>1 *)
p:=Prime[x]
sol:=Cos[p*ArcCos[m]]
sol1:=N[sol , acc]
sol2:=Rationalize[sol1]
ratio:=(sol2-m)/p
ask:=IntegerQ[ratio]
Table[ask , {x,2,100}]
{True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True,
True, True, True}