May 7, 2021
Can you find three distinct numbers such that the second is the square of the first, the third is the square of the second, and the first is the square of the third? Assuming you can, what are three such numbers?
Explanation:
Without the 'distinct' clause, we can easily think of two numbers, 0 and 1, who fit the description. But alas, is life ever that easy? Let us have a triplet,
Therefore, we are left to solve the following equation given that
Since
Adding complexity to the situation, no pun intended, we have 7 roots for the above polynomial equation. Of course, we must ignore the
When
So we have six triplets for
1 | ||||
2 | ||||
3 | ||||
4 | ||||
5 | ||||
6 |
This puzzle was "complex" after all!