A place to air possible concerns or difficulties in understanding ProjectEuler problems. This forum is not meant to publish solutions. This forum is NOT meant to discuss solution methods or giving hints how a problem can be solved.
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On my reading, there is no creative number, which can generate all integers >1.
(I have a non-formal prove for this in my mind)
As 0 gets rejected, this is obviously false.
I also initially believed there were no creative numbers, so I understand your frustration, but I do not believe it would be right to spoil your discovery of why this is false by providing one (nor, I imagine, do the problem creators, as they did not give such in the problem description).
On my reading, there is no creative number, which can generate all integers >1.
If it makes you feel better, I took about two days to convince myself that the answer was not 0. (I did have real work to do at the time too, or I might have been a bit quicker.)
Got it - and [here's a small hint nobody asked for]!
-> Completely solved: Thanks for the non-hints.
Did you really have to? Nobody other than you has asked for spoilers. People opening this thread expect to see clarifications about what the problem is asking and only that, you gave them an unexpected and unwelcome hint.
According to this Wikipedia article listing mathematical symbols, $\forall$ can be read as "for all", "for any", "for each", or "for every".
To me it was very clear that the meaning of "for any" in this problem is $\forall$, "for all", "for every"; rather than $\exists$, "for some", "there exists".
On the other hand, this answer on StackExchange gives some examples where the meaning of "any" is less clear, and one comment mentions a book on mathematical writing that discourages the use of "any" because of possible ambiguity.