How-many-divisors-has-the-positive-integer-n-which-verify-n-n-2027-2027-2028-

Question Number 158443 by HongKing last updated on 04/Nov/21

How many divisors has the positive

integer n which verify

n^{n} = 2027^{2027^{2028}} ?

Answered by MJS_new last updated on 04/Nov/21

{it}^{'} s easy to see that the solution of n^{n} = a^{a^{a + 2}}

is n = a^{a} . in this case n = 2027^{2027} . 2027 is

prime \Rightarrow 2027^{j} ∣ 2027^{2027}; 0 ⩽ j ⩽ 2027 \Rightarrow

we have 2028 divisors

Commented by HongKing last updated on 04/Nov/21

thank you so much my dear S er perfect