Find all positive real numbers x and nonnegative integers n such that:
x^{n}  āxā = n
*** ānā is the floor of n, which is equal to
the greatest integer less than or equal to n.
n = 0 works with 1 <= x < 2
n = 2 works with x = 2 or x = sqrt(3) = 3^(1/2)
n = 3 works with x = 2^(2/3) = 4^(1/3)
n = 4 works with x = 5^(1/4)
n = 5 works with x = 6^(1/5)
n = 6 works with x = 7^(1/6)
...
n = k works with x = (k+1)^(1/k)

Posted by Charlie
on 20240130 13:37:21 