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 April 9th, 2017, 06:27 AM #1 Banned Camp   Joined: Dec 2013 Posts: 1,117 Thanks: 41 Set of problems for fun Hi, Let p and q be prime numbers >=2 (q>p) Is there a way other than some program to solve : (1/p)^x + (1/q)^x=1 More generally is there a way to solve : sum((1/(p(i))^x(i))=1 with varying from 1 to n where p(i) is the ith prime x(i) is the ith variable solving the equation above. Example n=4 (1/2)^x(4) + (1/3)^x(4) + (1/5)^x(4) + (1/7)^x(4) = 1 Last questions : As n goes to infinite what is the limit of x(n)? To which set of numbers belongs x(i)? Thank you.
 April 9th, 2017, 11:00 AM #2 Banned Camp   Joined: Dec 2013 Posts: 1,117 Thanks: 41 Can you list the first 100 values of x(i) with a format x,xxxxxxxxxx (10 digits after the comma)? You have an infinite sequence of irrational numbers (x(i)) and there is (maybe?) a way to discover a closed formula for x(i). x(1)=0 x(2)=0.7878 (approximation) etc... Good luck! and good work!
 April 10th, 2017, 10:28 AM #3 Banned Camp   Joined: Dec 2013 Posts: 1,117 Thanks: 41 x(1000)=1.3957999 What about x(n) when n goes to infinite?
 April 11th, 2017, 04:49 AM #4 Banned Camp   Joined: Dec 2013 Posts: 1,117 Thanks: 41 Conjecture : As n goes to infinite x(n)=sqrt(2) If it is true then what?
 April 11th, 2017, 08:53 PM #5 Banned Camp   Joined: Dec 2012 Posts: 1,028 Thanks: 24 Pls rewrite in LaTex or it seems just a stupid question

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