What are the only two pairs of positive integers ( $$\(x, y\)$$ ) that satisfy $$\(x^{y}-y^{x}=1\)$$ ? Note: This is how to enter your answer. If your two ordered pairs are ( $$\(x_{1}, y_{1}\)$$ ) and ( $$\(x_{2}, y_{2}\)$$ ), please enter the value of $$\(x_{1}+y_{1}+x_{2}+y_{2}\)$$.

Mathematics
Competition
Math League
Exam No:2024 First Round Grades 10-12 Year:2024 Question No:28

Answer:

8

Knowledge points:

G10-12 - Number Theory - Diophantine Equations

Solution:

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