All Questions
5
questions
0
votes
1
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73
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Prime power decomposition
$x^{147} \equiv (((x^{7})^{7})^{3})\equiv x^{3}(mod7)$
How does $x^{147}$ simplify into $x^{3}(mod7)$
What Corollary is responsible for this?
Edit:
Fermat's Little Theorem is needed:
147 = 3 * 7 *...
- 289
2
votes
1
answer
71
views
Proof involving modular and primes
My Question Reads:
If $a, b$ are integers such that $a \equiv b \pmod p$ for every positive prime $p$, prove that $a = b$.
I started by stating $a, b \in \mathbb Z$.
From there I have said without ...
- 1,088
1
vote
1
answer
40
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Find $x$ such that $[x] \neq [0]$, $[x]\in\mathbb{Z}_n$, but $[x]^2=0$.
Find $x$ such that $[x] \neq [0]$, $[x]\in\mathbb{Z}_n$, but $[x]^2=0$. (Here $[x]$ denotes the equivalence class of $x$).
My goal here is to express $x$ in terms of $p$, a prime, and $m$, a natural ...
user322548
0
votes
1
answer
171
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Show that every prime factor of $4t^2 + 1$ is equivalent to 1 modulo 4
Show every prime factor of $4t^2 + 1$ is equivalent to 1 modulo 4
My working so far:
I want to use the first Nebensatz, so given q is a prime factor I want to show $(-1/q)=(-1)^{(q-1)/2}=1$ as this ...
- 621
0
votes
1
answer
495
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Generator of $Z_p^*$ with large p
I have to find a generator for $Z_{p}^*$. The prime number p is $2425967623052370772757633156976982469681$. My prime factors for (p-1) is according to 1 $f_k=(5,457,571,62429281,174394544633,...
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