Let and be positive integers such that . Find the minimum value of .
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From the equation above, we will get 8 y < 3 0 x < 9 y . As we need to keep the lowest y , we need to set the lowest x as well. Setting x = 1 gives 8 y < 3 0 < 9 y or 3 1 0 < y < 4 1 5 , which lies between 3.333... and 3.75. No integer y would be in between this range.
By setting x = 2 we will get 8 y < 6 0 < 9 y , or put it simply 3 2 0 < y < 2 1 5 This lies between 6.666 and 7.5, so the least positive integer y satisfying this inequality will be y = 7