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When is this sum nonzero?

0

$begingroup$

I am doing a problem whereby the proof is finished if I can find positive integers $h,h'$ such that:

beginequation sum_j=0^2n-1(-1)^j[cos((h+h')j fracpin) + cos((h-h')j fracpin)] neq 0 endequation

However I simply cannot find a way where this sum is nonzero, so I feel I may have constructed the proof incorrectly to lead to this requirement. I converted the equation into complex exponential however that didn't help me. Moreover wolfram alpha says it is zero. Any help would be great

summation

share|cite|improve this question

asked Mar 19 at 22:08

MatthewMatthew

337112

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  any constraint on $n$?
  $endgroup$
  – MoonKnight
  Mar 20 at 0:10
  

  
  
  
  

add a comment | 

0

$begingroup$

I am doing a problem whereby the proof is finished if I can find positive integers $h,h'$ such that:

beginequation sum_j=0^2n-1(-1)^j[cos((h+h')j fracpin) + cos((h-h')j fracpin)] neq 0 endequation

However I simply cannot find a way where this sum is nonzero, so I feel I may have constructed the proof incorrectly to lead to this requirement. I converted the equation into complex exponential however that didn't help me. Moreover wolfram alpha says it is zero. Any help would be great

summation

share|cite|improve this question

asked Mar 19 at 22:08

MatthewMatthew

337112

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  any constraint on $n$?
  $endgroup$
  – MoonKnight
  Mar 20 at 0:10
  

  
  
  
  

add a comment | 

$begingroup$

I am doing a problem whereby the proof is finished if I can find positive integers $h,h'$ such that:

beginequation sum_j=0^2n-1(-1)^j[cos((h+h')j fracpin) + cos((h-h')j fracpin)] neq 0 endequation

However I simply cannot find a way where this sum is nonzero, so I feel I may have constructed the proof incorrectly to lead to this requirement. I converted the equation into complex exponential however that didn't help me. Moreover wolfram alpha says it is zero. Any help would be great

summation

share|cite|improve this question

asked Mar 19 at 22:08

MatthewMatthew

337112

$endgroup$

share|cite|improve this question

asked Mar 19 at 22:08

MatthewMatthew

337112

share|cite|improve this question

asked Mar 19 at 22:08

MatthewMatthew

337112

asked Mar 19 at 22:08

MatthewMatthew

337112

asked Mar 19 at 22:08

MatthewMatthew

337112