# Divisible by 5?

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

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

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

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