+343 If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 131$, what is the minimal possible value of $|a - b|$?
+1950 Ok, so we start off with the equation
ab−3a+4b=131
I know this is random, but let'st ake the product of the coefficients on a,b.....add this product to both sides
So this gets us
ab−3a+4b+(4∗−3)=131+(4∗−3)ab−3a+4b−12=119
This eventually achieves the equation
(a+4)(b−3)=119
Now, the factors of 119 are 1,17,119
Since we want the minimum, let's use 7 and 17. We have
(13+4)(10−3)→|a−b|=|13−10|=3
Thus, our final answer is 3.
Thanks! :)
