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[tex]\sum_{n=0}^N cos(2\pi mn/N)cos(2\pi kn/N)=0[/tex]

where m != k, and 0<= m,k < N.

I couldn't prove this, so I plugged in specific values: N=4, m=1, k=3. I found that the sum equals 2. Likewise for other situations where m+k=N, it comes out non-zero.

Is the condition incorrect?