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Number Theory Level 2

If a^6 + b^6 = c^6 where a,b and c are consecutive integers, write the number whose value is equal to (a+c) x b


The answer is 0.

Mastermind Anirban by Mastermind Anirban , 38, India

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3 solutions

Rishabh Jain
Mar 3, 2014

its simple that the three consecutive integers are -1,0,1

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Adeetya Tantia
Apr 23, 2014

Due to Fermat's last theorem, all three cannot be positive integers... Therefore atleast one is negative with that the first that comes to mind is (-1,0,1) which fits and is the answer.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Very good! I like it even more than the above answer.

Eric Hernandez - 6 years, 10 months ago
Baby Googa
Feb 23, 2015

Fermat's last theorem has already been proven, so the integers are -1,0, and 1.

This makes the answer 0.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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