Quadratic Residues $\\pmod {2^n}$ - Mathematics Stack Exchange
2015年3月14日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Prove that $ (\mathbb {Z}_n , +)$, the integers $\pmod {n}$ under ...
Prove that $(\mathbb{Z}_n , +)$, the integers $\pmod{n}$ under addition, is a group. To show that this is a group, I know I need to show three things (in our text, we do not need to show that addition is closed-- rather, we show these three items): $(a)$ Associative Law $(b)$ Existence of Identity $(c)$ Existence of Inverse
elementary number theory - Calculate $11^ {35} \pmod {71 ...
From Fermat's little theorem (and the fact that quadratic polynomials have at most two roots mod a prime), you can conclude that $11^{35} \equiv \pm 1\mod 71$.
elementary number theory - Prove that if $p \equiv 3 \pmod {4}$, …
2015年2月25日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
elementary number theory - $x^2$ congruent to $1 \pmod {p ...
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modular arithmetic - How to calculate $2 ^ {-1} \pmod {10 ...
2018年9月24日 · Is there a way to do factorisation or some similar technique that ends with the same result like: $1/9 \pmod{10} = 1/3 \times 1/3 \pmod{10}$ and because 3 is comprime of 10 then is possible? Thanks modular-arithmetic
elementary number theory - How do I solve $32x \equiv 12 \pmod …
2017年9月9日 · I am able to solve simpler linear congruences, for example $3x \\equiv 2 \\pmod 5$. What I would do in this case is use that $0 \\equiv 10 \\pmod 5$ and then utilising a theorem: $3x \\equiv 12 \\pmod 5$...
number theory - Is $x^2 \equiv 1 \pmod{p^k} \iff x \equiv \pm 1 …
2018年3月16日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Find all four solutions to $x^2 \\equiv 133 \\pmod {143}$
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If $ab\\equiv ac\\pmod n$ and $a \\not\\equiv 0\\pmod n$, then …
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.