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Problem of the Day #22: Greatest Common Divisor Mod 2x+b April 10, 2011

Posted by Alex in : potd , trackback

Find the number of ordered pairs of positive integers $(a, b)$ such that $$\gcd(ax^2 + 36, 2x + b)\equiv\frac{72 – abx}{2}\pmod{2x+b}$$ as long as $x$ is a positive integer.

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