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April 9th, 2015, 10:35 AM  #1 
Newbie Joined: Oct 2013 Posts: 3 Thanks: 0  Recurrence sequence  proof
Hey, can you help me with this problem? Let m be positive integer and let's define a recurrence sequence: a(0)=a(1)=1, a(n+2)=a(n+1)+a(n)*e^(2πi*(n+1)/m). Prove that: a(2m)=a(m)+1 
April 9th, 2015, 03:30 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,034 Thanks: 1393 
Did you intend "m" to appear in the equation a(n+2) = a(n+1) + a(n)*e^(2πi*(n+1)/m)?

April 10th, 2015, 03:02 AM  #3 
Newbie Joined: Oct 2013 Posts: 3 Thanks: 0 
Yes, the sequence is dependent on the fixed m>=1


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proof, recurrence, sequence 
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