Understand the problem
Show that must be equal to or . Note: It is not required to show the existence of such numbers .
Source of the problem
Germany MO 2019, Problem 6
Start with hints
and then summing gives us that Our aim will be to reduce all the equations into a single variable. ( maybe a polynomial ). Let’s consider the case, where all of x,y,z is not 1.
as z is not equal to 1. Plugging the latter into the former and simplifying gives:
Now, observe that we already know z = 1 is a solution. This gives rise to
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