In this short set of numbers two do not belong:
1, 16, 64, 512, 4096, 46656, 1000000, 2985984
Why?
The numbers which belong have two special properties. Those not conforming have one of these which is not the same for each of them.
The numbers 16 and 512 do not belong.
All the other numbers corresponds to 6th power of an integer.
Thus, we have:
1=1^6 64 = 2^6 4096 = 4^6
46656 = 6^6 1000,000 = 10^6 2985984 = 144^6
However,
16 = 4^2, and 4 does not possess an integer cube root. Thus, 16 is not a perfect sixth power.
512 = 8^3, and 8 does not have an integer square root. Thus, 512 is not a perfect sixth power.
Edited on November 23, 2022, 12:19 pm
Puzzle Answer
