A and B

Number Theory Level 2

a a and b b are positive integers satisfying a + b = a b + b a a + b = \dfrac ab + \dfrac ba .

What is the value of a 2 + b 2 a^2 + b^2 ?


The answer is 2.

Achal Jain by Achal Jain , 19, India

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2 solutions

Keefe Sencen
Jun 15, 2019

juhst gues likee i dihd cuz it wurkd

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Christopher Ho
Mar 18, 2017

Instead of trying to solve this through algebra, we can find a pair of (a,b) that satisfy the equation.

We find that (1,1) works.

Substituting into the left side of the equation, we find that

a+b = 1+1 = 2

0 Helpful 0 Interesting 0 Brilliant 0 Confused

How did you arrive at the solution (1,1)? What is the intuition behind it?

Tapas Mazumdar - 4 years, 2 months ago

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