March Book of the Month is Unsolved Problems in Number Theory by Richard Guy, first published by Springer Verlag in 1981. Third edition (nearly three times the size!!) published in 2004.
These problems are mostly very easy to understand, but are as yet unsolved. Guy gives an account of the problems, and the progress made on them. He does this in such a way that they provide food for thought and avenues for exploration for mathematicians at varying levels of maturity in number theory.
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