Completely agree, I also liked the problem and thought it was conceptual as far as these things go.
Asking for N mod 1000 was another cute twist that was meant to get you thinking about the divisibility properties of the totient function - "hmm, so (p-1) always divides \phi(n) for all prime factors p of n, how convenient..."
The name of the twitter account is "نبض الفرات" which translates to "Euphrates pulse". However, you're right that the Twitter bio doesn't have that phrase; rather, in the link you gave it's another CENTCOM disclaimer. It looks like this phrase in the bio was later deleted and replaced with nothing (https://web.archive.org/web/20210506142008/https://twitter.c...), and probably not coincidentally the account is now suspended for breaking the Twitter rules.
From the link you gave, the bio of the "yemencurrent" account says "صفحة تابعة للقيادة المركزية الأمريكية لدعم الحوار حول الشأن اليمني و قضايا الأمن والاستقرارفي اليمن". I don't read Arabic, but google translates this as "A page affiliated with the US Central Command to support dialogue on Yemeni affairs and security and stability issues in Yemen". The documentcloud (https://www.documentcloud.org/documents/23466698) says that CENTCOM asked for a bluecheck and 'whitelisting' for the account. I don't see the big deal about this? After all, the account already indicated that it was government affiliated.
Edit: some else pointed out that the government may have been trying to trick Twitter by later deleting the disclaimer about affiliation. Looks like I should have read the article before posting!
It's worth pointing out that Gödel's axioms are commonly thought to be stronger than the existence of God (or gods, or "godlike objects") insofar as they entail modal collapse. Apparently, there are improvements of his argument that work around this, but I have never looked into them.
Asking for N mod 1000 was another cute twist that was meant to get you thinking about the divisibility properties of the totient function - "hmm, so (p-1) always divides \phi(n) for all prime factors p of n, how convenient..."