Taiwanese Math Olympiad 2000

Number Theory Level 3

y x 2 = x y + 2 y^{x^2} = x^{y+2} Determine all integral pairs ( x , y ) (x,y) that satisfy the equation above.

If the possible solutions can be expressed as ( a 1 , b 1 ) , ( a 2 , b 2 ) , … (a_1,b_1), (a_2,b_2), \dots , input the sum of all the coordinates as your answer.


The answer is 4.

Michael Huang by Michael Huang , 29, USA

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1 solution

Tom Engelsman
Apr 28, 2020

The required pairs include: ( x , y ) = ( 1 , 1 ) ; ( − 1 , − 1 ) ; ( 2 , 2 ) . (x,y) = (1,1); (-1,-1); (2,2). The coordinate sum calculates to 4 . \boxed{4}.

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