Fermat's Last Theorem for Binomial Coeffiecients

Number Theory Level pending

Let \( \mathbb{N}\) denote the set of natural numbers. Then does there exist, \( a,b,c,k \in\mathbb{N}\) , with \(k \geq 3\) such that \[ {a \choose k} + {b \choose k} = { c \choose k}. \] If no solution exists write \(0\) as an answer, if you think that this equation has a solution then find the value of \( a + b + c + k\).

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