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Proving Diophantine Equation has no solution using Legendre Symbol

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#number-theory #elementary-number-theory #diophantine-equations #legendre-symbol
87
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How to evaluate Legendre symbols more quickly

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#number-theory #prime-numbers #legendre-symbol
60
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Testing for primitive roots using quadratic non residue and Jacobi symbol

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#number-theory #quadratic-residues #primitive-roots #legendre-symbol
57
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Investigate the size of $\sum_{x=0}^{p-1}e^{2\pi ix^2/p}$

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#number-theory #analytic-number-theory #legendre-symbol
98
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Analogue of Fermat’s Theorem

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#number-theory #legendre-symbol
400
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If $(p^2-1)/8$ is an odd number and $p$ is prime odd number what is $p\pmod8$?

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#number-theory #elementary-number-theory #prime-numbers #modular-arithmetic #legendre-symbol
218
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Calculate Legendre symbol

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#number-theory #prime-numbers #modular-arithmetic #legendre-symbol
65
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Prove $\bigg(\frac{1(1-m)}{p}\bigg) + \bigg(\frac{2(2-m)}{p}\bigg) + \dots + \bigg(\frac{(p-1)(p-1-m)}{p}\bigg) = -1$.

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#elementary-number-theory #legendre-symbol
103
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Calculate Jacobi symbol

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#number-theory #legendre-symbol #jacobi-symbol
64
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Quadratic Integer Ring mod p - Field?

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#ring-theory #finite-fields #legendre-symbol #quadratic-integer-rings
74
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Finding solutions to $x^2\equiv a$ mod $8k+1$, $8k+1$ prime

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#elementary-number-theory #prime-numbers #modular-arithmetic #legendre-symbol #quadratic-reciprocity
285
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Product of Gauss sums $\tau_p,\tau_q$

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#elementary-number-theory #quadratic-residues #quadratic-reciprocity #legendre-symbol #gauss-sums
45
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What is the solution to $F\left(n\right)=F\left(n-1\right)+\left(\frac{2}{n}\right)F\left(n-2\right)$ with Legendre symbol?

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#recurrence-relations #legendre-symbol
27
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Verification: have I worked this legendre symbol correctly

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#legendre-symbol
363
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Find the primes $p$ such that the equation: $x^{2} + 6x + 15 = 0$ has a solution modulo $p$

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#elementary-number-theory #prime-numbers #modular-arithmetic #legendre-symbol

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