Trollathon 4-14

Level pending

Determine 201 4 T 2 ( m o d 10000 ) 2014^{T^2} \pmod{10000}

Note : You might want to refer to previous problems in order to solve this.


The answer is 2014.

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1 solution

Zi Song Yeoh
Apr 28, 2014

This link reveals the key. The note is just a red herring. Now, we can write 201 4 T 2 2014^{T^2} as ( 201 4 T ) T (2014^T)^T . So, by the first property of transpose (I know it only applies to matrix, but this is trollathon! XD), we have ( 201 4 T ) T = 2014 (2014^T)^T = 2014 .

8 T = 8 ^ T = \infty

Calvin Lin Staff - 7 years, 1 month ago

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WOAH!!!! I'm laughing so hard right now!!! XD

Aaghaz Mahajan - 2 years, 3 months ago

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