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AMO 2017 – Secondary 1 (Grade 7) Question 9

AMO · AMO 2017 – Secondary 1 (Grade 7)

Question 9

First, find all ordered pairs of integers $(x,y)$ satisfying $x^y=16$. Next, find the sum of all possible values of $x$ and the sum of all possible values of $y$. Finally, find the positive difference between the two sums.

Clarification: add the coordinates over all ordered pairs, counting a repeated coordinate once for each pair in which it occurs.

Question illustration