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If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 13$, what is the minimal possible value of $|a - b|$?

 Jan 13, 2024
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ab - 3a + 4b  = 13

 

ab + 4b  = 13 + 3a

 

b ( a + 4)  = 13 + 3a

 

b  =  (13 + 3a)  / (a + 4)

 

a must be odd for  b to  be  an integer

 

No integers avaiable

 

The function aproaches  3   when a is  large

 

When a = 1   b =  16/ 5  =  3.2  = b

 

And any odd "a"  > 1  will  result in   3 < b < 4     (not an integer)

 

 

cool cool cool

 Jan 13, 2024

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