^{1}+5

^{1}+12

^{1}=2

^{1}+9

^{1}+10

^{1}

4

^{2}+5

^{2}+12

^{2}=2

^{2}+9

^{2}+10

^{2}

Are equal power sum sets (EPSS) for second power, but the sum 4+5+12 is not the smallest. Find the smallest with all distinct positive integers.

Find EPSS of four numbers each (8 distinct positive integers) where the first, second *and* third powers have equal sums.

Keep going, if possible, to find higher order EPSS where fourth, fifth powers, etc. have equal sums.

Note: The highest EPSS I have is fifth power.