IndeterminateEquation Putnam

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Find all positive integers $n$ and $k_i$ $(1\le i \le n)$ such that $$k_1 + k_2 + \cdots + k_n = 5n-4$$ and $$\frac{1}{k_1} + \frac{1}{k_2} + \cdots + \frac{1}{k_n}=1$$

Solve in positive integers the equation $$3(xy+yz+zx)=4xyz$$

Solve in nonnegative integers the equation $$2^x -1 = xy$$