You are not wrong that it is true that if z(ab)=z(a)z(b) is true in binary, your condition will hold in any base - there are just occasional examples where it doesn't hold in the other direction.

Thanks, that looks interesting, though I am not sure if they are equivalent. E.g. 100010010 and 10010001 do not meet the condition of Z being multiplicative in binary, but do meet the condition of your problem in base 3 (product has only ones and zeros. (examples in base 10 might be very long)

I don't know if there is a simpler answer.

If every number in this set is unique (for your case 3,5,6,8,10,11}) the sum will only have zeros and ones. If any number is repeated, you will usually have a digit >1. However there will be some exceptions if the number of repeats is 0 or 1 MOD n, where n is your base.

OK. Well, in that case, I would offer this imperfect answer. Replace the two numbers you have with sets representing the positions of the ones. For your example 11010*100001 this would be {2,4,5} and {1,6}. Consider all the numbers you get from adding pairs of numbers taken from the two sets.

I am interested to see your answer! I can't think of a rule that deals in a simple way with carried digits.

Does your answer depend on the base being ten, or does it apply for any base >2?

Thanks, David!

www.youtube.com/shorts/NGJu6... Something like this?

Thank you!

Thank you!

I don't really understand why a table of contributions is bad. It seems like a straightforward way to give credit to people whose work contributed to the paper in different ways.