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

 Dec 5, 2020
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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

 Dec 5, 2020

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