# Do you need $$m$$?

$(1+x)^2+(1+x)^3+(1+x)^4+\cdots+(1+x)^{49} + (1+mx)^{50}$

Let $$m$$ be the minimum positive integer such that the coefficient of $$x^2$$ in the expansion above is $$(3n+1) \dbinom{51}{3}$$, where $$n$$ is an integer.

Find $$n$$.

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