Talk:Perfect totient number

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Hate to ask like this, but is this made up?

I have to ask if there's a level of obscurity to some of these concepts that are closer to original work (and goofiness) than they are to actually recognized concepts.Tgm1024 (talk) 15:54, 28 May 2014 (UTC)

Proof that every number reaches 1 in Iterated Totient Function

Every number iterates to 1 by Euler's Totient Function. Because 1 has phi(1) = 1, 2 has phi(2) = 1, and every other number has phi(n) < n (n = 2 also works) and by mathematical Induction, it works for 3, then 4, 5, 6, 7, 8, 9, 10, etc. and all the numbers.

This should be explained there. I have a theorem that if:

1. Finitely many numbers x have f(x) >= x.

2. Numbers having f(x) >= x have iterated function = y at last or form or lead to a loop or cycle of numbers.

Then: Iterated f(x) will never iterate unboundedly. y is the last number to reach. That, can be 1 most probably. But, sometimes like in Home Prime Sequence, it is prime number. 2409:40E0:104E:4773:8000:0:0:0 (talk) 17:14, 20 March 2025 (UTC)