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Is there a number which can be written in base 2,3,4,5,6 using only 0 and 1?

What's mind blowing here is that if you ask for base 2, 3, 4 the answers are trivial but for bases 2,3,4,5 somehow you get 82000 and we do not know whether there is another and for 6 it's unknown.



Am I missing something? the number 1 is 1 in all of those bases and therefore can be written using 0 (0 times) and 1 (1 time).


Sometimes mathematicians forget to say "non-trivial", that's what you're missing.


Often in mathematics, we look for the nontrivial solutions to questions like this.




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