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[x] equation

Source: Canada 1998

March 4, 2006
number theory unsolvednumber theory

Problem Statement

Determine the number of real solutions aa to the equation: [ 12  a ]+[ 13  a ]+[ 15  a ]=a. \left[\,\frac{1}{2}\;a\,\right]+\left[\,\frac{1}{3}\;a\,\right]+\left[\,\frac{1}{5}\;a\,\right] = a. Here, if xx is a real number, then [ x ][\,x\,] denotes the greatest integer that is less than or equal to xx.
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