Let the numbers be represented by "a" and "b". a < b 5a = 1 +3b Then a = (1 +3b)/5 So we can substitute for "a" to gete (1 +3b)/5 < b 1 +3b < 5b 1 < 2b 1/2 < b
The conditions will be met for any numbers "a" and "b" such that b > 1/2 a = (1 +3b)/5
Integer solutions will be solutions to the Diophantine equation 5a -3b = 1 which has solutions (for n ≥ 1) a = 3n -1 b = 5n -2 The smallest pair of integers meeting the requirement is 2 and 3.
