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If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 131$, what is the minimal possible value of $|a - b|$?

 Jun 21, 2024

Best Answer 

 #1
avatar+42 
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If we use SFFT to factor this expression, we get \((a+4)(b-3)=119\). Because 119 is 7*17, there are only limited cases. We are trying to get the smallest absolute value, meaning a=13 and b=10. Therefore, the minimal possible value of \(|a-b|\) is 3.

 

Feel free to tell me if I did anything wrong! :D

 Jun 21, 2024
 #1
avatar+42 
+1
Best Answer

If we use SFFT to factor this expression, we get \((a+4)(b-3)=119\). Because 119 is 7*17, there are only limited cases. We are trying to get the smallest absolute value, meaning a=13 and b=10. Therefore, the minimal possible value of \(|a-b|\) is 3.

 

Feel free to tell me if I did anything wrong! :D

Tottenham10 Jun 21, 2024

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