How to negate the following statement I am asking how to negate the following statement: For any positive $k$ there exists a number $N₀$ such that, for all $m≥N₀$, there exists a solution in positive integers to the equation: $$k/m=1/x+1/y+1/z$$

There exists a positive integer $k$ such that for any $N_0$ there exists $m \geq N_0$ with $\frac k m \
eq \frac 1 x+\frac 1 y+\frac 1 z$ for any choice of positive integers $x,y,z$.