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Find all $b$ such that $(a+b)^3 - a^3$ divisible $2007\ (a,b \in \mathbb{Z})$


I can solve for $b$: $(a+b)^3 - a^3=2007h \rightarrow b=\sqrt[3]{a^3+2007h}-a$

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    It might be more useful to think of this as $(a+b)^3-a^3=0$ mod $2007$.2012-12-21
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    Integer multiples of $b:=2007$ are solutions, Integer multiples of $b:=669$ are solutions. Could be more.2012-12-21
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    Also note that $2007 = 3^2 \times 223$, where $223$ is a prime.2012-12-21
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    and that $(a+b)^3 - a^3 = b (3 a^2 + 3 a b + b^2)$.2012-12-21
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    related : http://math.stackexchange.com/questions/188737/all-pairs-x-y-that-satisfy-the-equation-xyx3y3-3-20072012-12-21

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