Math_D
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Questions (13)

 7 Representing the function $\mathbb Z_9\to\mathbb Z_9$, $f(0) = 1$, $f(1) = \ldots = f(8) = 0$ as a polynomial in $\mathbb Z_9[x]$ 3 Is the number of quadratic nonresidues modulo $p^2$, greater than the number of quadratic residues modulo $p^2$? 3 Is the quadratic character, unique multiplicative character over $\mathbb Z_{p^n}$, for odd $p$? 3 Is $\sum\limits^n_{k=0}\frac{(y-0)(y-1)\cdots(y-n)}{y-k} \equiv 0 \pmod{n+1}$? 3 Walsh spectrum of a function defined over Galois rings

Reputation (175)

 +10 $\sum_{x \in \mathbb Z_9}w^{x^2-cx}=?$,where $c \in \mathbb Z_9$ and $w=e^{2\pi i/9}$ +5 What is the algebraic normal form of $F(x,y,z)= Trace (\alpha x^{24}) + x^{312} + yz$? +5 Representing the function $\mathbb Z_9\to\mathbb Z_9$, $f(0) = 1$, $f(1) = \ldots = f(8) = 0$ as a polynomial in $\mathbb Z_9[x]$ +5 Solve $r=(p-1)+pr_1+p^2r_2$ for $r_1$ and $r_2$ when $r(p-1) \equiv 1$ (mod $p^3$)

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 0 abstract-algebra × 5 0 galois-rings × 3 0 cryptography × 5 0 modular-arithmetic × 3 0 finite-fields × 4 0 number-theory × 3 0 finite-rings × 4 0 ring-theory × 3 0 elementary-number-theory × 3 0 roots-of-unity × 2

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