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Legendre Summations

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#number-theory #summation #legendre-symbol
42
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Legendre symbol trouble.

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#number-theory #legendre-symbol
1.5k
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Method of solving an Associated Legendre Equation with m=0, and m not equal to 0 with explanation

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#ordinary-differential-equations #legendre-polynomials #legendre-symbol #frobenius-method
573
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How to solve $1+\frac12-\frac13+\frac14-\frac15-\frac16+\frac18+\ldots+\left(\frac n7\right)\frac1n+\ldots$?

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#sequences-and-series #number-theory #algebraic-number-theory #legendre-symbol
174
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Numbers with prescribed Legendre symbols

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#number-theory #legendre-symbol
448
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$\tau( n!(n+1) ) = 2\times\tau(n!)$. Then what is $n!\;\text{mod} \; (n+1)?$

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#number-theory #elementary-number-theory #contest-math #factorial #legendre-symbol
310
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Quadratic residue equal to -1 for product of primes $ \equiv 1 \mod 4$

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#quadratic-residues #legendre-symbol
67
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Showing $\sum_{b=0}^{N-1}\left(\frac{b}{p}\right)\zeta_M^{-kb} = 0$

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#roots-of-unity #legendre-symbol
536
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How to prove this sum related to Legendre symbol

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#number-theory #legendre-symbol
169
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A generalization of a divisibility relation for Fibonacci numbers

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#prime-numbers #divisibility #fibonacci-numbers #conjectures #legendre-symbol
173
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Using Legendre's symbol to prove that $47$ is a factor of the Mersenne number, $M_{23}$

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#number-theory #prime-numbers #proof-explanation #legendre-symbol
132
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Legendre Symbol by Fermat's little theorem.

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#quadratic-residues #legendre-symbol
153
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Show that set of reduced residue classes is a subgroup of the multiplicative group of reduced residue classes

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#number-theory #quadratic-reciprocity #legendre-symbol #jacobi-symbol
1.2k
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How to prove that $7p + 3^p -4$ is not a perfect square?

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#number-theory #square-numbers #legendre-symbol
74
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$p$ an odd prime and $a,b\in\Bbb Z$ such that $ab\equiv 1\mod p$. Show that legendre symbols $({a\over p}) = ({b\over p})$

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#number-theory #elementary-number-theory #legendre-symbol

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