[seqfan] Takashi Agoh on Giuga's conjecture

[Paolo Lava]

In the article “On Giuga’s Conjecture”

(pages 506:504 in
http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN365956996_0087 ),
Takashi Agoh states that if n is a Giuga number (A007850) then for any
prime factor p of n we have:

i) pB(n-p)==p-1 (mod p^3)

ii) pB(n/p 1)==p-1 (mod p^2)

iii) pB(((n/p)-1)/p)==p-1 (mod p)

where B(i) is the Bernoulli number of index i.

I tried to compute some number that satisfy the above relations and I got
(Maple program):
i) 9, 25, 27, 45, 81, 125, 169, 225, 243, 325, 405, 625, 729, 1125, 2025,
2187, 2197, 3125, 3645,...
ii) 25, 125, 169, 325, 625, 2197, 3125, 4225...
iii) ?

No Giuga number at all: for sure there must be something I misinterpret...

Paolo