MathDB
S 20

Source:

May 25, 2007
floor functionMiscellaneous Problems

Problem Statement

Let nn be a positive integer that is not a perfect cube. Define real numbers aa, bb, cc by a=n3,  b=1a−⌊a⌋,  c=1b−⌊b⌋.a=\sqrt[3]{n}, \; b=\frac{1}{a-\lfloor a\rfloor}, \; c=\frac{1}{b-\lfloor b\rfloor}. Prove that there are infinitely many such integers nn with the property that there exist integers rr, ss, tt, not all zero, such that ra+sb+tc=0ra+sb+tc=0.
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