SOLUTION: For what positive integers n greater than or equal to 2 is {{{root(n,a^n)}}}{{{""=""}}}{{{a}}} always a true statement?

Algebra.Com
Question 767750: For what positive integers n greater than or equal to 2 is always a true statement?
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!


It is always true ONLY when n is odd.

[It is true when n is an even number as long as
"a" is not a negative number, but it's false when
n is even and a is a negative number]

Edwin




RELATED QUESTIONS

For a positive integer $n$, $\phi(n)$ denotes the number of positive integers less than... (answered by ikleyn,math_tutor2020)
for a given even whole number n, the expression n-2 represents and even whole number... (answered by richard1234)
Use mathematical induction to prove each statement is true for all positive integers n:... (answered by math_helper)
The expression 1/1.2 + 1/1.3 + 1/1.4 +......+ 1/n(n+1) for any natural number n is (a)... (answered by solver91311)
Determine whether a statement n^2 + n + 401 is prime for every natural n is true or... (answered by ikleyn)
If n is any positive odd integer greater than 1, the n(n^2 – 1) is always divisible by: (answered by richwmiller)
Find the sum a + (a + 1) + (a + 2) + ... + (a + n - 1) in terms of a and n. Part... (answered by ikleyn)
Identify a counterexample to disprove each statement, where "n" is a real number. (answered by richwmiller)
Use mathematical induction to prove the statement is true for all positive integers n. (answered by Edwin McCravy)