mersenneforum.org Congruent to 10^n mod 41
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 2020-01-09, 11:56 #1 enzocreti   Mar 2018 20D16 Posts Congruent to 10^n mod 41 215, 51456, 69660, 92020 and 541456 are the k's such that pg(k) is prime and k is congruent to 10^n mod 41 for n some nonneg integer I think it is surprising that in the case k is NOT a multiple of 3 (k=215, 92020, 541456) Then (k-10^n)/41 is a number A such that inserting a 0 in each pair of adjacent digits it turns out to be a multiple of A. Example (541456-10)/41=13206. Inserting a 0 in each pair of adiajent dig its you have 103020006 which is a multiple of 13206. The thing doesn't work when k is a multiple of 3 as in the cases 69660 and 51456 Last fiddled with by enzocreti on 2020-01-09 at 12:09

 Similar Threads Thread Thread Starter Forum Replies Last Post enzocreti enzocreti 0 2019-06-27 12:31 smslca Math 2 2012-01-29 11:30

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