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May
7
answered Finite abelian groups of order 100
May
7
answered Group of $2n$ elements, $n$ odd, is not simple
May
6
revised At the point $\sqrt{2}$ in the real line, does *every* n-ball around that point contain a rational?
deleted 3 characters in body
May
6
answered At the point $\sqrt{2}$ in the real line, does *every* n-ball around that point contain a rational?
May
6
comment Formula for $r+2r^2+3r^3+…+nr^n$
Oh dayum, this is nice.
May
6
comment Formula for $r+2r^2+3r^3+…+nr^n$
If you take it to infinity then yes.
May
6
answered Prove that if $\{1^5,2^5,\ldots, (pq)^5\}$ is a complete residue system mod $pq$, then $\{1^5,2^5,\ldots,p^5\}$ is a complete residue system mod $p$.
May
5
comment What are the primary disadvantages of Dummit and Foote's abstract algebra text (3rd ed.)?
I don't know if this is a disadvantage though.
May
5
comment What are the primary disadvantages of Dummit and Foote's abstract algebra text (3rd ed.)?
It has almost no category theory.
May
5
comment Example of a monomorphism and epimorphism that is not isomorphism.
I wouldn't call them exact duplicates
May
5
awarded  Favorite Question
May
5
answered In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all element non zero in $A$ is invertible.
May
5
revised not sure how to do this
edited tags
May
5
comment Let $f(x) = x^2 + x + 41$. Show that $f(n)$ is prime for $0 \le n \le 39$, but $f(40)$ is composite.
No, because you didn't prove the induction can help you prove it for $n=5$ by assuming it is true for $n=1,2,3,4$. You only proved it when the assumption is that it is true for $n=1,2,3\dots 38$ and you want to prove it for $39$. So the induction never even starts.
May
5
comment Is the condition of PID necessary?
I don't know, this is the proof I know, but I don't think you can prove it straight-forwardly.
May
5
answered Prove $A\cap (B-C) = (A\cap B) - (A\cap C)$
May
5
comment Let $f(x) = x^2 + x + 41$. Show that $f(n)$ is prime for $0 \le n \le 39$, but $f(40)$ is composite.
You didn't do your induction correctly. You have to prove that if a statement is true for all positive integers smaller than $n$ then it is also true for $n+1$. You just proved the particular case when $n$ is $39$. You have to prove it for arbitrary values of $n$ so that the induction works. Of course it is impossible to prove it for arbitrary values of $n$, since it is not true for all valuse of $n$. Induction is used to prove statements for all natural numbers, you only want to prove the statement for some values of $n$, this is why induction won't work.
May
5
comment Is the condition of PID necessary?
Oh right, I remember my teacher did this a couple of weeks ago, but I wasn't paying much attention. Thank you very much, this process has been very profitable for myself also.
May
5
revised Is the condition of PID necessary?
added 13 characters in body
May
5
comment show $p$ is divisible by $(x^2 +y^2 +1)$
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