April 9th, 2017, 06:27 AM  #1 
Senior Member Joined: Dec 2013 Posts: 1,101 Thanks: 40  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 
Senior Member Joined: Dec 2013 Posts: 1,101 Thanks: 40 
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 
Senior Member Joined: Dec 2013 Posts: 1,101 Thanks: 40 
x(1000)=1.3957999 What about x(n) when n goes to infinite? 
April 11th, 2017, 04:49 AM  #4 
Senior Member Joined: Dec 2013 Posts: 1,101 Thanks: 40 
Conjecture : As n goes to infinite x(n)=sqrt(2) If it is true then what? 
April 11th, 2017, 08:53 PM  #5 
Senior Member Joined: Dec 2012 Posts: 951 Thanks: 23 
Pls rewrite in LaTex or it seems just a stupid question


Tags 
fun, problems, set 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How to master maths  should we solve simple problems or variety of problems?  joshis1  Algebra  2  October 10th, 2014 03:55 PM 
3 problems.  helpme93  Elementary Math  15  June 20th, 2014 01:04 AM 
problems  joserizal  Math Events  8  December 19th, 2013 10:48 AM 
4 problems  storybookending  Algebra  7  July 14th, 2013 09:53 PM 
Log problems and word problems help  thenewkid77  Algebra  1  March 11th, 2010 07:27 AM 