OFFSET
0,1
COMMENTS
For k not divisible by 5, k is a fifth power in 5-adic field if and only if k == 1, 7, 18, 24 (mod 25). If k is a fifth power in 5-adic field, then k has exactly one fifth root.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
Wikipedia, p-adic number
EXAMPLE
The unique number k in [1, 5^5] such that k^5 - 7 is divisible by 5^6 is k = 1047 = (13142)_5, so the first five terms are 2, 4, 1, 3 and 1.
MAPLE
op([1, 3], padic:-rootp(x^5-7, 5, 100)); # Robert Israel, Aug 28 2019
PROG
(PARI) a(n) = lift(sqrtn(7+O(5^(n+2)), 5))\5^n
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Jianing Song, Aug 28 2019
STATUS
approved