# Try bashing

Number Theory Level 5

$$\sqrt{10y^{2}-2b^{2}-8by} = x$$

$$y$$ is the repeated root(at least two roots are same) of the function $$y^{3}-12y+c$$ and $$b$$ is any number and c is positive

Let $$p$$ be total number of different integral values of $$x$$ ; (q) be sum of all different integral values of $$x$$ ; $$r$$ be number of integral values that $$b$$ can take to get an integral $$x$$ .

Find $$p + q + r + c$$

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