MathDB

Prove that for every positive integer

t

there is a unique permutation

a_0, a_1, \ldots , a_{t-1}

0, 1, \ldots , t-1

such that, for every

0 \leq i \leq t-1

, the binomial coefficient

\binom{t+i}{2a_i}

is odd and

2a_i \neq t+i

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