Papers › On Integers Whose Sum is the Reverse of their Product
On Integers Whose Sum is the Reverse of their Product
Xander Faber, Jon Grantham
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We determine all pairs of positive integers (a,b) such that a+b and a ×b have the same decimal digits in reverse order: (2,2), (9,9), (3,24), (2,47), (2,497), (2,4997), (2,49997), … We use deterministic finite automata to describe our approach, which naturally extends to all other numerical bases. Our automata are a variation on the notion of Young graphs, which were introduced by Sloane to study ``reverse multiples''.
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