If n is a root of the equation x^{2}+px+m=0 and m is a root of the equation x^{2}+px+n=0, where m \neq n, then what is the value of p+m+n?

Explanation

Substituting the roots into their respective equations gives n^2 + pn + m = 0 and m^2 + pm + n = 0. Subtracting the second equation from the first yields (n^2 - m^2) + p(n - m) - (n - m) = 0. Since m \neq n, we can divide by (n - m) to get n + m + p - 1 = 0, which implies p + m + n = 1.

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