Today is 10/07/2014

Find the sum of all integers x x such that ( 10 x 20 + 7 x 14 ) (10x^{20}+7x^{14}) is divisible by 2014 \displaystyle 2014 .

2014 0 Infinite 7

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1 solution

This might look tricky at first. But it is not that much.

Notice x \displaystyle x has only even powers. If x = a x=a is a solution, then x = a x=-a is another solution.

So the sum of all solutions becomes 0 \boxed{0} .

Exactly! Took me 5 5 secs. :3

Jubayer Nirjhor - 6 years, 8 months ago

Beautiful and awesome!!

Adarsh Kumar - 6 years, 8 months ago

You tricky little SOB, I almost made a huge mistake, nice prob.

Nafees Zakir - 6 years, 8 months ago

Did the same! Exactly! Nice!

Kartik Sharma - 6 years, 8 months ago

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