N is a 4-digit positive integer such that the sum of the four digits of N equals the product of the first two digits of N and also equals the product of the last two digits of N.
Find all N's and prove there are no others.
is easily found that there cannot exist
an abcd solution with three or four digits distinct.
A generic abab solution will generate the
abba, baba , baab solutions. <br>
3. Write 2*(a+b)-a*b
as a =2*b/(b-2), which produces integer values for b=3 or 4 or
We get generic answers: (a,b ) = (3,6); (4,4 ); (6,3 ).
set of all valid answers is: (4,4,4,4); (3,6,6,3); (3,6,3,6); (6,3,6,3); );(6,3,3,6);
General remark: Finding all Ns constitutes
a full proof there are no others.