13th Root

Author

Eric W. Weisstein
August 19, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Algebra/13thRoot.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/13thRoot.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Examples

100-Digit

(random=With[{n=100},Table[Random[Integer,{Ceiling[(10^(n-1))^(1/13)],Floor[(10^n-1)^(1/13)]}]^13,{10^4}]]);//Timing

Length[IntegerDigits[#]]&/@random//Union

Timing[roots=#^(1/13)&/@random][[1]]/Length[random]

Take[roots,10]

And@@Equal@@@Transpose[Take[#,10]&/@{roots^13,random}]

200-Digit

(random=With[{n=200},Table[Random[Integer,{Ceiling[(10^(n-1))^(1/13)],Floor[(10^n-1)^(1/13)]}]^13,{10^4}]]);//Timing

Length[IntegerDigits[#]]&/@random//Union

Timing[roots=#^(1/13)&/@random][[1]]/Length[random]

Take[roots,10]

And@@Equal@@@Transpose[Take[#,10]&/@{roots^13,random}]