Here is very interesting result that I found about number 9 and
sum of digits.
Sum of digits of the sum of 9+any integer is the integer itself. or
Sum of digits of the sum of number 9 and any integer is the sum of
digits of added integer. Let sod sum of digits
If 9+x = y then x = y(sum of digits of sum)OR
If 9+(10a+b)=10m+n then a+b = m+n OR
If 9 + sigma(AnXn) = sigma(BnXn)then sigma(An) = Sigma(Bn)
If x is single digit integer Let 9 + x = 10a+b then x = a + b
e.g. 9+1 = 10 sod = 1+0 = 1 and added integer is 1.
9+2 = 11 sod = 1+1 = 2 and added integer is 2
9+3 = 12 sod = 1+2 = 3 and added integer is 3
Let sod1 = sum of digits of added integer
and sod2 = sum of digits of the result after addition
9+11 = 20 then sod1 = 1+1 = 2 = sod2 = 2+0=2 = 2
9+13 = 22 then sod1 = 1+3 = 4 = sod2 = 2+2 = 4
I may be reinventing the wheel. But this theorem is characterists od
definition of decimal number system. If there are 8 digits in a
number system(octal)then 8 + any integer may result in same manner.
For binary system 0,1 therfore, binary 1 + any binary integer may
yield similar results. This is also true for prime numbers also.
If anyone is interested in sum of digits and properties of number
system do write me.
D M kulkarni