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Old 2018-01-29, 13:16   #2
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"Forget I exist"
Jul 2009

203008 Posts

Originally Posted by lukerichards View Post
Hi all,

I've found a sequence of numbers which I have submitted to OEIS. Other contributors have taken an interest and found a simpler generating function to mine...

... except none of us know *why* it works. We don't want to include the function on the entry until we can explain why the simpler function outputs the same results.

Essentially it comes down to this:

Why is:

3^k+2\equiv0 \pmod {3^x+2} (k>x)

equivalent to

3^k \equiv -1 \pmod {3^x+2} (k>x)

The sequence was defined using the first equivalence, but a pari script, which works in a way equivalent to the second equivalence, generates the same numbers in a fraction of the time. But I'm not enough of a number theorist to ger my head around it!
Edited the second one. To make more sense to me.
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