If a and b are positive integers for which ab - 3a + 5b = 137 what is the minimal possible value of |a - b|?

ab - 3a +5b = 137

a = (137 - 4 5)/(b - 3), or: b = (3 a + 137)/(a + 5) For positive solutions, I see only 2 as follows: a =56 and b=112 a=143 and b=89 From the 3 above, the one with smallest absolute difference is: abs[112 - 56] = 27