Difficult discrete-time periodicity problem

[jti5017]

Homework Statement

Determine whether x[n] is periodic, if so find the fundamental period.

ps forgive my notation, I'm new to physics forums and haven't had a chance to figure out the exact notation syntax yet.x[n]=cos(π/6 * n^2)

The Attempt at a Solution

x(n) is periodic when x(n) = x(n +N)x(n+N) = cos(π/6 * (n+N)^2)

π/6(2*n*N + N^2) = k*2*π

this is kinda where i got stuck

(2*n*N + N^2) = 12 * k

 

[tiny-tim]

welcome to pf!

hi jti5017! welcome to pf!

try using the X² button just above the Reply box

is it true for the same N, for all n ? ​

 

[jti5017]

thanks for the reply!

it has to be true for all n to be periodic by definition i believe.
i mean, I've personally never heard of a sinusoidal period being a function of time (in this case discrete time)

And there are an infinite number of 'N's (provided it is periodic) but I am specifically looking for the lowest N, the fundamental period