1,942 reputation
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location Trondheim, Norway
age 26
visits member for 3 years, 5 months
seen 1 hour ago

I fancy topology.


2d
comment Suppose that p and q are twin primes. Show that if x^2≡p (mod q) is solvable then so is x^2≡q (mod p)
@JonathanMckibbin: they are equivalent. Just note that the RHS is always 1 (since one of $(p-1)/2)$ and $(q-1)/2$ has to be even). Now if one term on the LHS is 1, then consequently the other term as to be as well. It is a straightforward application of the theorem.
2d
comment Inequality proof, why isn't squaring by both sides permissible?
You are applying what you are trying to prove. Clearly, the statement is "obvious" but if I ask you: why is it that $0<a<b$ then $a^2 < b^2$? The mathematical proof is what you outline above.
2d
answered Suppose that p and q are twin primes. Show that if x^2≡p (mod q) is solvable then so is x^2≡q (mod p)
2d
comment Suppose that p and q are twin primes. Show that if x^2≡p (mod q) is solvable then so is x^2≡q (mod p)
Hm.. What results do you know?
Apr
17
comment Critical points and Convexity?
What is $M$? --
Apr
17
comment Fraction Problem. 3rd grader question got parents thinking
This is correct, but not very accessible. Unfortunately, I cannot see any way around it without introducing some equivalently complex computations.
Apr
17
comment Example of $\liminf_{n\rightarrow\infty}(x_n+y_n)>\liminf_{n\rightarrow\infty}x_n+\liminf_{n\rightarrow\infty}y_n$
@mjh: sure but, $1,2,3,\ldots \pmod \pi$ comes arbitrarily close
Apr
17
comment Example of $\liminf_{n\rightarrow\infty}(x_n+y_n)>\liminf_{n\rightarrow\infty}x_n+\liminf_{n\rightarrow\infty}y_n$
$-1, -1, -\sqrt{2}$.
Apr
17
answered Example of $\liminf_{n\rightarrow\infty}(x_n+y_n)>\liminf_{n\rightarrow\infty}x_n+\liminf_{n\rightarrow\infty}y_n$
Apr
17
comment Example of $\liminf_{n\rightarrow\infty}(x_n+y_n)>\liminf_{n\rightarrow\infty}x_n+\liminf_{n\rightarrow\infty}y_n$
$x_n = \sin(n)$ and $y_n = \cos(n)$?
Apr
16
comment Counterexamples in set theory
If $x\in A\cap B\cap C$ then surely $x\in A\cap B$ etc. also
Apr
10
comment deduce the Cup product structure RP^n with Z coefficient from Z_2 coefficient
I cannot find this statement on page 214?
Apr
8
comment The number of edges this graph
How do you get {24, 26, 36} from {2,3,4,6}?
Apr
7
comment Inductions and proofs
$2^{n-1} + 2^{n-2} + 2^{n-3} = 2^{n-3}(4 + 2 + 1) \leq 2^{n-3}2^3$
Apr
6
revised Condition about regular graphs
added 131 characters in body
Apr
6
comment Condition about regular graphs
Interesting, did not know that it had a name. Thanks.
Apr
6
comment Does the rank-nullity theorem extends to vector spaces of infinite dimension?
It also generalizes vastly using category theory: en.wikipedia.org/wiki/Splitting_lemma
Apr
6
comment Condition about regular graphs
@bof: Oops. Fixed!
Apr
6
revised Condition about regular graphs
added 9 characters in body
Apr
6
revised Condition about regular graphs
added 95 characters in body