Does positive integer n have positive integer factors a and b such that ab = n and a - b = 1?
(1) When n is divided by 10, the remainder is 3
(2) n = 19,073
(1) n = (2x * 5y) + 3; where x and y are integers. When n = 13, although ab (1*13) = n, but a- b >1. Again when n = 63, which can be prime factorized as 3^2 * 7, ab = n ,but a - b > 1. So, n can be expressed as a product of an integer with unit digit of 1 and 3, the difference between its 2 factors will always be greater than 1. Sufficient.
(2)
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(1) When n is divided by 10, the remainder is 3
(2) n = 19,073
(1) n = (2x * 5y) + 3; where x and y are integers. When n = 13, although ab (1*13) = n, but a- b >1. Again when n = 63, which can be prime factorized as 3^2 * 7, ab = n ,but a - b > 1. So, n can be expressed as a product of an integer with unit digit of 1 and 3, the difference between its 2 factors will always be greater than 1. Sufficient.
(2)
...
