Is Pascal's triangle valid in non-decimal systems?

Question

Does it conserve all its properties if we consider all systems with a base different from 10?

Answer 1

The entries in Pascal's triangle are just numbers -- they are not numbers are in any particular base.

You can choose to write those numbers down in base ten, or base seventeen, or in Roman numerals or English words. That does not change which numbers they are, and every property of the triangle that only depends on which numbers are in it will work the same no matter how you choose to write down those numbers.

Purely typographical "properties" that speak of your representation of numbers rather than what the numbers themselves are -- such as "how many digits there are in row 17" -- will of course change with your choice of representation.

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                          eins
                     eins      eins
                eins      zwei      eins
           eins      drei      drei      eins
      eins      vier      sechs     vier      eins
 eins      fünf      zehn      zehn      fünf      eins