Divisible by 5?

There is a math teacher in a school whose favorite number is a positive integer (let's call it x).x). She told her 5 students--Alice, Beatrice, Candice, Denise, Eunice--the number x,x, and the following conversation took place:

Alice: "x+1x+1 is not divisible by 5."
Beatrice: "x+2x+2 is not divisible by 5."
Candice: "x+3x+3 is not divisible by 5."
Denise: "x+4x+4 is not divisible by 5."
Eunice: "x+5x+5 is not divisible by 5."

Without knowing xx, can we guarantee that at least one of these 5 students is lying?

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