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: Question: 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:

1910667181420507984555759916338506
= 2*3*7*43*1831*138683*2861051*1456230512169437
by M. Hogan and C. Mangilin

4200017949707747062038711509670656632404195753751630609228764416142557211-
582098432545190323474818
=2*3*11*23*31*47059*2217342227*1729101023519*
8491659218261819498490029296021*58254480569119734123541298976556403
by R. Girgensohn.

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