Really! Its different!

Number Theory Level 3

If a,b are positive integers then let K \bf K be the number of solutions of the equation a 2016 + b 2016 = 201 6 2016 a^{2016} +b^{2016}= 2016^{2016} ,

Then find the value of [ 2016 K ] \bf [2016K] .

[ . ] \bf [.] denotes greatest integer function.


The answer is 0.

Samarth Agarwal by Samarth Agarwal , 21, India

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1 solution

Samarth Agarwal
Jan 5, 2016

This problem has a one line solution..... By Fermat's last theorem, there is no solution of this equation...That's it!!

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Exactly.

Why did you make it [2016K]?

Dev Sharma - 5 years, 5 months ago

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some people have a habit to guess the answer using 0,1 etc so... :P

Samarth Agarwal - 5 years, 5 months ago

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