Number Theory

$\begin{matrix} \left( 1782^{ 12 }+1841^{ 12 } \right) ^{ \frac { 1 }{ 12 } } & = & 1922 \\ 1782^{ 12 }+1841^{ 12 } & = & { 1922 }^{ 12 } \end{matrix}$

This violates Fermat's last theorem.

Note: this answer is just an elaboration of Nurul's answer

In an apparent glance,

Your mind & your helping device may deceive you.

The Fermat's Last Theorem will be violated if the equation is true.

On the other side the sum of these two numbers where one of them is even and other one is odd should be an odd number. But the number is in the right side is absolutely falsely placed.

We all know that when the power of any two variables is same then we take it common. By this we can solve this. [{(1782+1841)/\12} /\ (1/12)] in this power 12 will be cancelled by 1/12 because when there are two power on the same base then powers are multiplied. So, 12 * 1/12 = 1 and when we add 1782 & 1841 we get (3623)/\1 or 3623 not 1922. So this is false.