Question

The function $f(n) = \sum_{d \mid p_n\#} \mu(d)\sum_{r^2 = 1\mod d}\lfloor\frac{p_{n+1}^2 - 2 - r}{d}\rfloor$ has no fixed point $f(n) = n$?

score 45 · Answer 1 · 2023-10-30 01:32:01

45

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The function $f(n) = \sum_{d \mid p_n\#} \mu(d)\sum_{r^2 = 1\mod d}\lfloor\frac{p_{n+1}^2 - 2 - r}{d}\rfloor$ has no fixed point $f(n) = n$?

Published on 30 Oct 2023 - 1:32

score 90 · Answer 2 · 2026-02-23 06:39:41

90

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score 54 · Answer 3 · 2023-11-02 20:41:26

54

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166

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78

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36

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64

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100

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score 38 · Answer 9 · 2024-02-08 19:14:39

38

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score 47 · Answer 10 · 2024-02-11 01:52:21

47

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score 56 · Answer 11 · 2026-02-23 06:40:54

56

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score 21 · Answer 12 · 2024-02-22 14:38:06

21

Views

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135

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score 138 · Answer 14 · 2024-02-28 11:40:37

138

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score 223 · Answer 15 · 2022-06-25 02:37:23

223

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List Question

The function $f(n) = \sum_{d \mid p_n\#} \mu(d)\sum_{r^2 = 1\mod d}\lfloor\frac{p_{n+1}^2 - 2 - r}{d}\rfloor$ has no fixed point $f(n) = n$?

A tight positivity conjecture about sums over divisors of square-free integers.

Rearrange the terms in the alternating harmonic series such that the sum is $s \in \mathbb{R}$

How do you find the value of $\sum_{n=1}^{\infty} (-1)^{n+1}\frac{1}{n^2}$?

An identity involving alternative sum of triple product of binomial coefficients

alternate series convergence

Property of the alternating operator

How to deduce: $T(x_1, \dots , x_i+x_j, \dots, x_i+x_j, \dots , x_n) = 0$?

What does it mean, The space $L_n (V^n;K)$ of alternating n-linear forms is of dimension one?

On the fractional parts of the roots of the Alternating Harmonic Numbers

What is the 1-case closed form for $\sum_{i = 1}^{x} \lfloor \frac{i - r}{d}\rfloor$?

$\sum_{j=0}^\infty(-1)^j\frac{1 -e^{(aj^2 + b)M}}{1-e^{aj^2 +b}}$?

Why is a=43 an exception?

Alternating sum of reciprocals of binomial coefficients

Proving $(ac+bd)^2+(ad-bc)^2=(a^2+b^2)(c^2+d^2)$ with various solutions.

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