A New Year's challenge

[soroban]

Find the next equation in the sequence:

. . $\begin{array}{ccc}3^2 + 4^2 &=& 5^2 \\ 3^3 + 4^3 + 5^3 &=& 6^3 \\ \vdots && \vdots \end{array}$

 

[Opalg]

Find the next equation in the sequence:

. . $\begin{array}{ccc}3^2 + 4^2 &=& 5^2 \\ 3^3 + 4^3 + 5^3 &=& 6^3 \\ \vdots && \vdots \end{array}$

The next equation is " $3^4 + 4^4 + 5^4 + 6^4 = 7^4$ ". The text in between says "But it is not true that".

Happy New Year to all at MHB! (d)