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- #1

- Feb 14, 2012

- 3,963

**happy and Merry Christmas**,

**much luck**,

**good health**and

**all good things of life**. I hope you guys are able to spend it with loved ones!

I want to also present a "Christmas Math Challenge" as a gift to my friends (all of you are my friends, aren't you?) here today!

$a$ satisfies the equation $\left(a+\dfrac{1}{a}+1 \right)\left(a+\dfrac{1}{a} \right)=1$.

What is the value of $\left(a^{20}+\dfrac{1}{a^{20}}+1 \right)\left(a^{20}+\dfrac{1}{a^{20}} \right)$?