List questions from quadratic-reciprocity

Published on 06 Feb 2019 - 22:24

283

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If $d$ divides $a^4+a^3+2a^2-4a+3$, prove that $d$ is a fourth power modulo $13$

Published on 30 Mar 2019 - 11:44

89

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Prove that if $a^{(n-1)/2}\equiv\pm1\pmod{n}$, then $\left(\frac{a}{n}\right)\equiv a^{(n-1)/2}\pmod{n}$

Published on 23 Mar 2026 - 6:48

243

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Show that $n = 3^{100} + 2$ is not a prime number.

Published on 14 Apr 2019 - 14:47

119

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A Fibonacci Number problem(please help me that 1 answer is mine)

Published on 27 Apr 2019 - 16:31

74

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Generalization of Jacobi symbol for composite $n$

Published on 22 Mar 2026 - 19:29

196

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Quadratic reciprocity and decomposition of primes in cyclotomic fields

Published on 25 Mar 2026 - 3:24

324

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Quadratic reciprocity in Langlands program

Published on 22 Mar 2026 - 13:45

68

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Solution to equation modulo p

Published on 22 May 2019 - 10:14

49

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Proving that $n$ is not a prime

Published on 21 Jun 2019 - 12:43

50

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Question on modular arithmetic with prime numbers

Published on 21 Jun 2019 - 13:34

91

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Why if the Legendre symbol satisfy $\left(\frac{a}p\right)=\left(\frac{p}a\right)$ then $\left(\frac{a}p\right) = 1$?

Published on 24 Jun 2019 - 20:03

129

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Assume that p and q are odd primes and $p \equiv q \pmod {28}$. Show that $(\frac{7}{p}) = (\frac{7}{q})$.

Published on 24 Jun 2019 - 22:25

73

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"Inverting" the Artin map in terms of characters

Published on 01 Jul 2019 - 16:55

123

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How to evaluate $\prod_{n=1}^{p-1} \sin(\frac{2n^2\pi}{p})$

Published on 22 Aug 2019 - 5:37

List Question

Is there a proof of quadratic reciprocity using $p$-adic numbers?

If $d$ divides $a^4+a^3+2a^2-4a+3$, prove that $d$ is a fourth power modulo $13$

Prove that if $a^{(n-1)/2}\equiv\pm1\pmod{n}$, then $\left(\frac{a}{n}\right)\equiv a^{(n-1)/2}\pmod{n}$

Show that $n = 3^{100} + 2$ is not a prime number.

A Fibonacci Number problem(please help me that 1 answer is mine)

Generalization of Jacobi symbol for composite $n$

Quadratic reciprocity and decomposition of primes in cyclotomic fields

Quadratic reciprocity in Langlands program

Solution to equation modulo p

Proving that $n$ is not a prime

Question on modular arithmetic with prime numbers

Why if the Legendre symbol satisfy $\left(\frac{a}p\right)=\left(\frac{p}a\right)$ then $\left(\frac{a}p\right) = 1$?

Assume that p and q are odd primes and $p \equiv q \pmod {28}$. Show that $(\frac{7}{p}) = (\frac{7}{q})$.

"Inverting" the Artin map in terms of characters

How to evaluate $\prod_{n=1}^{p-1} \sin(\frac{2n^2\pi}{p})$

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