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Some powers decomposed (Posted on 2015-04-16) Difficulty: 3 of 5
Consider
S1=9 = 1! + 2! + 3!
S2=27 = 1! + 2! + 4!
S3=32 = 2! + 3! + 4!

The S1, S2, S3 represent the values of integer powers that can be represented as a sum of exactly three distinct factorials (0! excluded)

Find S4, S5, S6.

A friendly tip: STOP after S6.

No Solution Yet Submitted by Ady TZIDON    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re: Thoughts from OEIS | Comment 4 of 5 |
(In reply to Thoughts from OEIS by Jer)

The factorials get large fast, and even the prospect of factoring say 30-digit numbers can be daunting, especially since UBASIC, which is capable of handling such large numbers, is interpreted (and, further, emulated via DOSBox  if using windows 7 or later), together with the noted difficulty of factoring non-primes with two large factors.
  Posted by Charlie on 2015-04-17 11:43:19

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