perplexus.info :: Numbers : Some powers decomposed

Some powers decomposed (Posted on 2015-04-16)

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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answer

| Comment 1 of 5

S4 = 128 = 2! + 3! + 5! = 2⁷ S5 = 841 = 1! + 5! + 6! = 29² S6 = 5184 = 4! + 5! + 7! = 72² "(It is inferred that the "integer powers" are powers greater than 1. That is, 123 = 1! + 2! + 5! = 123¹ has been excluded as its integer power representations are limited to the first power).

Posted by Dej Mar on 2015-04-16 15:49:46

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