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Define a bad dice to be a fair dice with 13 sides numbered 1 through 13, inclusive. (That is, each of the 13 sides lands with equal probability). When Jeffery ...

Call an ordered pair of positive integers \( (x, y) \) dead if \( (x-y)(x^2+xy+y^2)-xy=61 \). Find the sum of all \( x+y \) over all dead pairs ...

If \( f(x) \) is a monic polynomial of degree 10 such that \( f(x)=x^2 \) for \( x=1, 2, \ldots, 10 \), then find the value of \( f(11) \)

Given that \[f(x)=x^4+10 x^3+35 x^2+50 x+24\] and that ...

Find the last 3 digits of the number of solutions to ...

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