Problems & Puzzles: Puzzles

Puzzle 327. Giuga numbers

Perhaps you already know what the Giuga numbers are (*). A short definition would be this one:

Giuga numbers n: p|(n/p-1) for every prime divisor p of n.

  Nowadays there are only eleven known of them.

The smallest and the largest are 30 (3 prime factors) & 554079914617070801288578559178 (8 prime factors)

(see Sloane's A007850)

Among the many very attractive question arising around the Giuga numbers I will just select one of them:


Compute one more Giuga number (the 12th?)

(In doing so, I will strongly recommend at least to read the following article)

(*) This puzzle came after some discussion about the Giuga numbers with my friend A. Rupinski.

Other Giuga numbers (12th & 13th?) can be found here:

= 2*3*7*43*1831*138683*2861051*1456230512169437
by M. Hogan and C. Mangilin

by R. Girgensohn.


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