Binomial Number

Author

Eric W. Weisstein
February 8, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Combinatorics/BinomialNumber.nb.

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

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

Table

(a^n)-(b^n)

Table[{n,Factor[a^n-b^n]},{n,32}]//TableForm

(a^n)+(b^n)

Table[{n,Factor[a^n+b^n]},{n,32}]//TableForm

Number of Terms in Factorization

Length/@Table[FactorList[a^n-b^n],{n,30}]-1

Length/@Table[FactorList[a^n-1],{n,30}]-1

Length/@Table[FactorList[a^n+b^n],{n,30}]-1

Length/@Table[FactorList[a^n+1],{n,30}]-1

Factors of (a^(2^n))+(b^(2^n))

Table[{n,Factor[(a^(2^n))+(b^(2^n))]},{n,7}]//ColumnForm

Table[{n,Factor[(a^(2^n))+1]},{n,7}]//ColumnForm