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Well, it definitely is not Dostoyevsky's famous saying in Russia.
I think the most "appropriate" novel for such a discourse about living with or without hope is "The House of the Dead"...

Rockzmom, if the phrase is a google hit, and especially not in the native language of the one who "said" that, it doesn't mean yet that it really is his famous saying. :) It-ogo is right, this...

I am sort of a fan of Dostoyevsky, but I don't know this "quote". It is not a famous saying, definitely.