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Jan
21
comment Applying iterated function on the sum of the squares of the prime factors of $30$
Actually that last one is tricky. Not sure I agree. What I would say is that if $n$ is sufficiently large (50K or so) f(n) will be greater than 30. This lemma if true only deals with first iterates. So suppose $n = 50000.$ Then $f(n)$ will be greater than 30. Suppose $f(n)$ is much less than 50000. Then I think $f(f(n)$ might be less than 30.
Jan
21
comment Applying iterated function on the sum of the squares of the prime factors of $30$
I think it is possible to show that $\frac{2\ln n}{\ln 2}< f(n)\leq n^2.$ Then for example we need look no farther than $n = 50000$ to find $f(n) = 30.$ Not very useful.
Jan
21
revised How did Gauss discover the prime number theorem?
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Jan
20
answered How did Gauss discover the prime number theorem?
Jan
18
comment Why were proofs avoiding complex analysis preferred in number theory? Is this distinction still important?
@Mathemagician1234: Fine (I didn't downvote btw) but I'm not sure your post conveys this.
Jan
18
revised Sum of the divisors of $n$, related to the Hardy-Littlewood circle method
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Jan
16
comment If $a,b,c$ are real numbers all less than or equal to $1$ such that $a+b+c=0$ , then is it true that $(1-a)(1-b)(1-c) \le 1$?
You have received 7000+ points worth of votes and have not cast a single vote...?
Jan
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revised Sum of the divisors of $n$, related to the Hardy-Littlewood circle method
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Jan
16
comment Why were proofs avoiding complex analysis preferred in number theory? Is this distinction still important?
@Mathemagician1234: You have posted some really nice answers but this one seems anhistorical. Adam Hughes' observation that the distinction became "less of a community preoocupation over time" is certainly correct. But Selberg didn't get a Fields medal for wrestling with an "anachronism dating from the 18th century." When Ingham reviewed Erdos' and Selberg's papers he used the term transcendental to refer to complex methods. There was a feeling that the power of complex methods transcended elementary methods. That sense has faded but I don't think it was ever seen as silly.
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