Number theory · Continued fractions · Integer part · Division with remainder
Natural numbers \(a\), \(b\) and \(c\) satisfy
\[ a + \cfrac{1}{b + \cfrac{1}{c}} = \frac{4016}{2007} . \]
Prove that
\[ \cfrac{1}{c + \cfrac{1}{b + \cfrac{1}{a}}} = \frac{2007}{4016} . \]
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Serbian Municipal Competition 2007, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source