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bio website fkraiem.org
location Bordeaux, France
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visits member for 3 months
seen Apr 20 at 11:59

Mar
26
comment Question over proving normal subgroups
Actually, you also need to prove that $Z(G)$ is non-empty (and generally the easiest way to show that a subset of a group is non-empty when we want to show that it is a subgroup is to show that it contains the identity).
Mar
15
answered How to solve equations with modulus in them
Mar
12
comment square numbers multiplied by non-square numbers
@MJD The answer, maybe. The "explanation", maybe not.
Mar
12
comment square numbers multiplied by non-square numbers
What kind of "numbers" are we talking here?
Mar
12
comment Primes modulo which an algebraic equation admits a solution
It seems also that a root of $X^4+10X^2+5$ in $\mathbf{F}_p$ is always primitive (i.e., has multiplicative order $p-1$). Sorry, I can't investigate further, it is late here.
Mar
12
comment Primes modulo which an algebraic equation admits a solution
Experimentally, it seems true that if $X^4 + 10X^2 + 5$ has a root in $\mathbf{F}_p$, then $5$ divides $p-1$ (equivalently, $p \equiv 1 \pmod {10}$).
Mar
12
comment Primes modulo which an algebraic equation admits a solution
Not sure what you are asking... $p = 11$ and $r = 8$ works.
Mar
12
answered Why would you define $i$ as $i^2=-1$, and why not as $i=\sqrt{-1}$?
Mar
11
comment A proof using Fermat's Little Theorem?
p \nmid a $p \nmid a$ (you should also use \mid for "divides": $k \mid (p+1)$).
Mar
11
comment Notation Question regarding Ring-mod-Number and Ring-mod-Some Kernel
Do you know what an ideal is in a ring?
Mar
11
comment Show p(X) (over a field) is irreducible iff p(X+a) is irreducible
The "standard" proof that a map is an automorphism will work, there is really no special trick. (Just remember that $P(X+a)$ is not the same thing as $P(X)+a$.)
Mar
11
comment Show p(X) (over a field) is irreducible iff p(X+a) is irreducible
What can you say about the map $p(X) \mapsto p(X+a)$ from $A[X]$ to itself?
Mar
11
comment Setting every $k^{th}$ bit of a number to zero
Sorry, I was thinking in binary... Fixed.
Mar
11
revised Setting every $k^{th}$ bit of a number to zero
deleted 2 characters in body
Mar
10
comment Finding all subrings with identity of $\mathbb Z_{16}$
You can start by looking for its subgroups...
Mar
10
comment What would be $\left(\mathbf{v} + \mathbf{u}\right)^2$?
Terminology point: "solve" should normally only be used for (in)equations. You can say "solve $3x+2=0$ (for $x$)" or "solve $A\mathbf{u} = \mathbf{v}$ (for $A$, given $\mathbf{u}$ and $\mathbf{v}$)", but "solve $(\mathbf{v}+\mathbf{u})^2$" is essentially the same as "solve $2$": there is nothing to solve for. The verb you want is "determine" or "compute".
Mar
10
comment Discrete Math Testing Cardinality
Can't you see a bijection betwen these two sets?
Mar
9
comment listing elements of equivalence class
No. $m$ is equivalent to $n$ if and only if $m^2-n^2$ is a multiple of $3$, or equivalently if and only if $m^2-n^2 \mod 3 = 0$. Now, what does it mean for $n$ to be equivalent to $0$?
Mar
9
comment listing elements of equivalence class
Well, what does it mean for an integer $n$ to be equivalent to $0$?
Mar
9
comment Which greedy algorithm is optimal?
For a), yes, you have to show it mathematically. However, since you have to show that it is not optimal, you just need to give a counterexample. Given the hint, I suggest you try with $n = 2$.