## Problem of the Week 1036## Rational CoincidenceHow many rational numbers a/b are there (with a and b relatively prime) such that a/b = b.a where the dot is interpreted as the usual base-10 dot? That is, you seek positive integers a and b such that the base 10 number obtained by placing b and a side-by-side with a decimal point between them exactly equals a/b.
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Extra Credit: Suppose we work in base B. So now we ask for two integers such that the rational number a/b is identical to the rational obtained as b.a in base B, meaning b + (a / B Conjecture: 10 is the first base for which there exists two relatively prime integers a and b so that a/b is identical with b.a. [View the solution] |

12 September 2005