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If a and b are positive integers for which ab - 3a + 4b = 137 what is the minimal possible value of |a - b|?

 Jul 1, 2018
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ab - 3a + 4b = 137

 

a = (137 - 4 b)/(b - 3), or:
b = (3 a + 137)/(a + 4)
For positive solutions, I see only 3 as follows:
a =1 and b=28
a=21 and b=8
a=121 and b=4
From the 3 above, the one with smallest absolute difference is:
abs[21 - 8] = 13

 Jul 1, 2018

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