+1278 If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 131$, what is the minimal possible value of $|a - b|$?
+129881 ab -3a + 4b = 131 take the product of the coefficients on a,b.....add this product to both sides
ab - 3a + 4b + (4 * - 3) = 131 + (4 * -3)
ab - 3a + 4b - 12 = 119 factor the left side
(a + 4) ( b - 3) = 119
Factors of 119 are 1 7 17 119
Using 17 and 7
( 13 + 4) ( 10 - 3) → l a - b l = l13 - 10 l = 3
