A number theory problem by Md Zuhair

Number Theory Level 2

If x x and y y are non-negative integers satisfying x y + x − y = 8 xy+x-y=8 , find all the solutions of ( x , y ) (x,y) .

( x , y ) = ( 5 , 6 ) , ( 6 , 5 ) (x,y) = (5,6), (6,5) ( x , y ) = ( 2 , 5 ) , ( 2 , 7 ) (x,y) = (2,5), (2,7) ( x , y ) = ( 3 , 9 ) , ( 1 , 4 ) (x,y) = (3,9), (1,4) ( x , y ) = ( 8 , 0 ) , ( 2 , 6 ) (x,y) = (8,0), (2,6) ( x , y ) = ( 7 , 8 ) , ( 7 , 8 ) (x,y) = (7,8), (7,8)

Md Zuhair by Md Zuhair , 20, India

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2 solutions

Kay Xspre
Feb 24, 2016

We rewrote it to ( x − 1 ) ( y + 1 ) = 7 (x-1)(y+1) = 7 To which the answer would be ( x , y ) = ( 8 , 0 ) , ( 2 , 6 ) , ( 0 , − 8 ) , ( − 6 , − 2 ) (x,y) = (8,0), (2,6), (0,-8), (-6, -2) in integers. Since we need natural number, we pick only the first two as answer.

8 Helpful 0 Interesting 0 Brilliant 0 Confused

Did the same. 😀😀

Anurag Pandey - 4 years, 10 months ago
Rishik Jain
Feb 25, 2016

You shoul refrain from giving choices in these kind of questions.

4 Helpful 0 Interesting 0 Brilliant 0 Confused

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