Simple Alzebra

Number Theory Level 3

Let a a and b b be distinct positive integers satisfying a b = a 2 − b 2 ab=a^2-b^2 . Find the number of possible pairs of ( a , b ) (a,b) .


The answer is 0.

Akash Shukla by Akash Shukla , 26, India

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1 solution

Michael Mendrin
Jun 3, 2016

Solve for b b to get b = 1 2 ( − 1 ± 5 ) a b=\dfrac { 1 }{ 2 } \left( -1\pm \sqrt { 5 } \right) a and see if you can get any integer solutions besides 0 , 0 0,0

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