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Just Browsin'


Dec
9
awarded  Caucus
Dec
9
awarded  Popular Question
Nov
26
comment Two questions on number 2013
@Lokesh: Robert Israel clarified it. Both -3 and 3 are odd numbers. So adding the plus or minus sign is not going to change their oddness or evenness. In other words, 'Sum of an odd number of odd numbers is odd.'
Nov
26
comment Two questions on number 2013
@lokeshsangabattula: I doubt people are going to spell out every detail here. Alistair has given an answer so that you can compare it to yours. Try to write out all the elements of the set $S_{2013}$. You can easily guess it by seeing the pattern and then prove your guess by induction.
Nov
6
accepted Maximal commutative subring of the ring of $2 \times 2$ matrices over the reals
Nov
6
accepted An identity that is always an integer
Nov
5
comment A contest inequality
I have tried that.The case with 2 is trivial. Even with just two terms(case where 2014 is replaced by 4),I have no idea what to do.
Oct
1
awarded  Popular Question
Sep
30
awarded  Explainer
Sep
29
awarded  Tumbleweed
Sep
28
awarded  Yearling
Sep
26
comment Given $f:[0,1]\to[0,1]$ and $q:[0,1]\to\mathbb{R}$, is there a $g$ such that $q(f(x))\equiv g(q(x))$?
The commutative diagram in the title is very disconcerting.
Sep
24
awarded  Autobiographer
Sep
23
comment What Gauss *could* have meant?
In the spirit of Gauss' quotes, I would have replied "The result was apparent to me immediately: but I do not yet know how I am to arrive at them."
Sep
22
asked Pre-requisites for 'The Concept of a Riemann Surface'
Sep
22
comment Is it true that $n^2+3n+13$ is prime for all $n\in\mathbb ℤ^+$?
@Nilan: $n = a+b+1$? Hint: replace $n$ by $n+1$ ;)
Sep
18
comment An identity that is always an integer
:) This was my generalization. In fact, any symmetric polynomial is a polynomial in elementary symmetric polynomials and here the elementary symmetric polynomials are integers, so every symmetric polynomials in those fractions are integers. I want to obtain a problem where proving an identity is an integer is hard when we use these tricks. In this way I can motivate Gauss symmetric polynomial theorem. Thanks for the answer :)
Sep
18
comment How to find identity and inverse for the group $(\mathbb{Z}, \ast)$, where $a \ast b = a+b-ab$
This 'one' is worse than the real 'one'. The real one does not harm any element after it acts, but this one gobbles up everything it sees :P
Sep
18
asked An identity that is always an integer
Sep
18
comment How to determine the orbits of points under the tripling map $f(x)=3x\bmod 1$?
Also notice that $\frac{3^2}{72} = \frac18$. So if $\frac18$ is periodic and $\frac1{72}$ does not appear in its orbit, what do you think will happen to $\frac1{72}$? Can it be periodic?