Correct Option: C

Given x(n) = e	jnπ	cos		nπ
	16			17

Fundamental period of

x1(n) = e	jnπ
	16

or x1(n) = cos	nπ	+ j sin	nπ
	16		16

N1 =	2πm	=	2π	· m = 32
	Ω		π
			16

Fundamental period of

x2(n) = cos			nπ
			17

i.e., N2 =	2πm	=	2π	· m = 34
	Ω		π
			17

Fundamental period of the signal
x(n) = GCM of N₁ and N₂
= GCM of 32 and 34

=	32 × 34	= 544
	2

Hence, alternative (C) is the correct choice.