Inspired by some popular book about Fermat's Last Theorem years ago, experimented a bit and found some interesting sequence:
$3 \neq 4$
$3^2 + 4^2 = 5^2$
$3^3 + 4^3 +5^3 = 6^3$
$3^4 + 4^4 + 5^4 + 6^4 \neq 7^4$
Inspired by some popular book about Fermat's Last Theorem years ago, experimented a bit and found some interesting sequence:
$3 \neq 4$
$3^2 + 4^2 = 5^2$
$3^3 + 4^3 +5^3 = 6^3$
$3^4 + 4^4 + 5^4 + 6^4 \neq 7^4$
Looks like it was nothing to explain about. Since I originally failed to observe that first expression is inequalty, it looked interesting to me that sequence breaks at order of 4 (and is fulfilled for the first 3). After first expression correction, it was pointless.