[seqfan] Re: Primes of the form (4^p+1)/5^t
Don Reble
djr at nk.ca
Wed Mar 15 04:00:57 CET 2017
> Let N=(4^p+1)/5^t, where p is prime, 5^t is the most power of 5 dividing
> 4^p+1. For p=2,3,5, N=17,13,41. What is the next prime p for which N is
> prime?
To prove there aren't any more prime N's, a first step is to
show that if 5^n divides either of (2^(2a+1) +- 2^(a+1) + 1),
then 5^(n-1) divides (2a+1). Calculations suggest it's true,
but I'm stuck.
--
Don Reble djr at nk.ca
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