1970 Canadian MO Problems/Problem 1
Find all number triples such that when any of these numbers is added to the product of the other two, the result is .
From the first equation minus the second, we get :
So either or . For , since the equations were symmetric, we have one solution of . From , substituting it into the original three derived equations, we have: We then get Substituting this into , Thus, either , or . Since the equations were symmetric, we then get the full solution set of:
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