proof that the set of sum-product numbers in base 10 is finite
This was first proven by David Wilson, a major contributor to Sloane’s Online Encyclopedia of Integer Sequences.
First, Wilson proved that (where is the number of digits of ) and that
. The only way to fulfill the inequality is for .
Thus, a base 10 sum-product number can’t have more than 84 digits. From the first integers, we can discard all those integers with 0’s in their decimal representation. We can further eliminate those integers whose product of digits is not of the form or .
|Title||proof that the set of sum-product numbers in base 10 is finite|
|Date of creation||2013-03-22 15:46:58|
|Last modified on||2013-03-22 15:46:58|
|Last modified by||PrimeFan (13766)|
|Synonym||Proof that the set of sum-product numbers in decimal is finite|