## Num3er 666 and equal sums and sum of 5-th powers

$666 = 100+105+106+116+117+122 = 101+102+110+112+120+121$

$100^5+105^5+106^5+116^5+117^5+122^5 = 101^5+102^5+110^5+112^5+120^5+121^5$

Note that

$n+(5+n)+(6+n)+(16+n)+(17+n)+(22+n)$
$= \; (1+n)+(2+n)+(10+n)+(12+n)+(20+n)+(21+n)$

$n^5+(5+n)^5+(6+n)^5+(16+n)^5+(17+n)^5+(22+n)^5$
$= \; (1+n)^5+(2+n)^5+(10+n)^5+(12+n)^5+(20+n)^5+(21+n)^5$