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You play a game with your friend. He flips 2014 coins, while you flip 2015 coins. Whoever gets more tails wins; however, if you tie, your friend wins. What is ...

Find all polynomials \(P(x) = a_n x^n + a_{n-1} x^{n-1} \dots + a_1 x + a_0\) such that \(a_n \neq 0\), \((a_n, a_{n-1}, \dots, a_1, a_0)\) is a permutation ...

Find the sum of all (possibly negative) integers \(n\) such that

\[n^2+2 \mid 2014n+2.\]

\(N\) is a number where integers from 1 through 60 are written continuously, thus \(N=1234567891011...585960.\) What is the largest possible number that could be made after 100 digits ...

Consider the sequence defined by \(a_k = \frac{1}{k^2+k}\) for \(k \geq 1\).

Given that ...

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