Question by Summer Clouds - Discuss with MathYouLike

Summer Clouds moderators

04/08/2017 at 09:21

Let a, b, c, d , e are integers satisfying the following expression:
\(\dfrac{501}{2015}=\dfrac{1}{a+\dfrac{1}{b+\dfrac{1}{c+\dfrac{1}{d+\dfrac{1}{e}}}}}\)

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CTC 04/08/2017 at 09:26

Okay :0

\(\dfrac{501}{2015}=\dfrac{1}{\dfrac{2015}{501}}=\dfrac{1}{4+\dfrac{11}{501}}=\dfrac{1}{4+\dfrac{1}{\dfrac{501}{11}}}=\dfrac{1}{4+\dfrac{1}{45+\dfrac{6}{11}}}=\dfrac{1}{4+\dfrac{1}{45+\dfrac{1}{\dfrac{11}{6}}}}=\dfrac{1}{4+\dfrac{1}{45+\dfrac{1}{1+\dfrac{5}{6}}}}=\dfrac{1}{4+\dfrac{1}{45+\dfrac{1}{1+\dfrac{1}{\dfrac{6}{5}}}}}=\dfrac{1}{4+\dfrac{1}{45+\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{5}}}}}\)

So (a;b;c;d;e) = (4;45;1;1;5)
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