List questions from quadratic-reciprocity

Published on 10 Apr 2026 - 17:06

73

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Show that $z^2$ is a fourth power mod $q$ if and only if $\left(\frac{z}{q}\right) = 1$, given that $q \equiv 1 \pmod{4}$.

Published on 15 Apr 2026 - 19:32

50

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Intuition behind Eisenstein's proof of quadratic reciprocity using a function of a complex variable

Published on 09 Apr 2026 - 8:33

84

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prime divisors of number of the form $32z^4+1$

Published on 15 Apr 2026 - 15:53

61

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Stuck in a quadratic reciprocity problem

Published on 12 Apr 2026 - 20:45

39

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Determining which primes satisfy a set of quadratic divisibility conditions

Published on 14 Apr 2026 - 22:04

52

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Conceptual explanation for extra/missing $p$ solutions to $x^2+y^2=a \pmod p$ at $a=0$

Published on 16 Apr 2026 - 14:46

49

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How to show a quadratic polynomial with complex roots has solutions mod $p$?

Published on 10 Apr 2026 - 17:34

77

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How to prove the roots of $ax^2 + bx + a$ are reciprocals of each other?

Published on 11 Apr 2026 - 16:53

109

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Quadratic Reciprocity

Published on 14 Apr 2026 - 1:35

86

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For which n does a quadratic congruence have solutions e.g $x^2=83 (modn) $

Published on 14 Apr 2026 - 19:37

578

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Evaluating quadratic residue $(6/p) $

Published on 15 Apr 2026 - 12:57

50

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Averages of $L(1,\chi)$

Published on 16 Apr 2026 - 2:36

63

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For which primes $p$ does $x^2\equiv3\pmod{p}$ have a solution?

Published on 15 Apr 2026 - 8:37

964

Views

A conjecture about quadratic residues given $p \equiv 5 \pmod 8$

Published on 14 Apr 2026 - 16:42

List Question

Generalized Pépin-Test (Problem understanding a paper)

Show that $z^2$ is a fourth power mod $q$ if and only if $\left(\frac{z}{q}\right) = 1$, given that $q \equiv 1 \pmod{4}$.

Intuition behind Eisenstein's proof of quadratic reciprocity using a function of a complex variable

prime divisors of number of the form $32z^4+1$

Stuck in a quadratic reciprocity problem

Determining which primes satisfy a set of quadratic divisibility conditions

Conceptual explanation for extra/missing $p$ solutions to $x^2+y^2=a \pmod p$ at $a=0$

How to show a quadratic polynomial with complex roots has solutions mod $p$?

How to prove the roots of $ax^2 + bx + a$ are reciprocals of each other?

Quadratic Reciprocity

For which n does a quadratic congruence have solutions e.g $x^2=83 (modn) $

Evaluating quadratic residue $(6/p) $

Averages of $L(1,\chi)$

For which primes $p$ does $x^2\equiv3\pmod{p}$ have a solution?

A conjecture about quadratic residues given $p \equiv 5 \pmod 8$

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