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 Power x mod x (Posted on 2008-12-18)
Find the smallest positive integer, x, such that 2x (mod x) = 3.

 See The Solution Submitted by pcbouhid Rating: 4.0000 (1 votes)

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 computer assisted and researched solution | Comment 3 of 5 |
`10 for x=1 to 2020     ?x,(2^x)@x30 next`
`finds this sequence`
`1       02       03       24       05       26       47       28       09       810      411      212      413      214      415      816      017      218      1019      220      16`

Putting the terms into Sloane's  The On-Line Encyclopedia of Integer Sequences! gives sequence A015910, which links to A050259 to list the x values that lead to a remainder of 3. That sequence starts 1, 4700063497, 3468371109448915, 8365386194032363, meaning that in the current context, 4,700,063,497 is the answer.

 Posted by Charlie on 2008-12-18 22:21:47

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