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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