OFFSET
0,2
COMMENTS
10-adic integer x=.....86760045215487480163574218751 satisfying x^3=x.
A "bug" in the decimal enumeration system: another square root of 1.
Let a,b be integers defined in A018247, A018248 satisfying a^2=a,b^2=b, obviously a^3=a,b^3=b; let c,d,e,f be integers defined in A091661, A063006, A091663, A091664 then c^3=c, d^3=d, e^3=e, f^3=f, c+d=1, a+e=1, b+f=1, b+c=a, d+f=e, a+f=c, a=f+1, b=e+1, cd=-1, af=-1, gh=-1 where -1=.....999999999. - Edoardo Gueglio (egueglio(AT)yahoo.it), Jan 28 2004
What about the 10-adic square roots of -1, -2, -3, 2, 3, 4, ...? They do not exist, unless the square really is a square (+1, +4, +9, +16, ...). Then there's a nontrivial square root; for example, sqrt(4)=...44002229693692923584436016426479909569025039672851562498. - Don Reble, Apr 25 2006
REFERENCES
K. Mahler, Introduction to p-Adic Numbers and Their Functions, Cambridge, 1973.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..9999
FORMULA
(a_0 + a_1*10 + a_2*10^2 + a_3*10^3 + ... )^2 = 1 + 0*10 + 0*10^2 + 0*10^3 + ...
For n > 0, a(n) = 9 - A091661(n).
EXAMPLE
...4218751^2 = ...0000001
MATHEMATICA
To calculate c, d, e, f use Mathematica algorithms for a, b and equations: c=a-b, d=1-c, e=b-1, f=a-1. - Edoardo Gueglio (egueglio(AT)yahoo.it), Jan 28 2004
CROSSREFS
KEYWORD
base,nonn,nice,easy
AUTHOR
Robert Lozyniak (11(AT)onna.com), Aug 03 2001
EXTENSIONS
More terms from Vladeta Jovovic, Aug 11 2001
STATUS
approved