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A264008
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Index of the smallest Fibonacci number divisible by prime(n)^2.
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1
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6, 12, 25, 56, 110, 91, 153, 342, 552, 406, 930, 703, 820, 1892, 752, 1431, 3422, 915, 4556, 4970, 2701, 6162, 6972, 979, 4753, 5050, 10712, 3852, 2943, 2147, 16256, 17030, 9453, 6394, 5513, 7550, 12403, 26732, 28056, 15051, 31862, 16290, 36290, 18721, 19503, 4378, 8862, 49952, 51756, 26106, 3029, 56882, 28920
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OFFSET
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1,1
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LINKS
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FORMULA
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MAPLE
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f:= proc(n) local p, phi, q, k, G, Fkm, Fk, M, W, m;
p:= ithprime(n);
if member(p mod 5, {1, 4}) then
phi:= rhs(op(msolve(x^2-x-1, p^2)[1]));
q:= -1-phi mod p^2;
return numtheory:-order(q, p^2);
fi;
G:= GF(p, 2, alpha^2-alpha-1);
q:= G:-ConvertIn(-1-alpha);
k:= G:-order(q);
Fkm:= combinat:-fibonacci(k-1) mod p^2;
Fk:= combinat:-fibonacci(k) mod p^2;
M:= <<Fkm, Fk>|<Fk, (Fkm+Fk mod p^2)>>;
W:= <0, 1>;
for m from 1 do
W:= M . W mod p^2;
if W[1] = 0 then return(m*k) fi
od:
end proc:
f(3):= 25:
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PROG
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(PARI) a(n) = if(n==3, 25, my(p=prime(n)); fordiv(p^2-1, d, if(fibonacci(d)%p==0, return(d*p)))); \\ Altug Alkan, Oct 31 2015
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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