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visits member for 2 years, 7 months
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I fill in "About Me" sections from time to time.


Jan
22
comment Heat Equation, possible solutions
If no specific f is given and you are just asked to find any solution, you can pick and f you want.
Jan
7
answered Are $\frac{a}{\gcd(a,n)}$ and $n$ always relatively prime?
Jan
5
answered Why if matrix $A$ is invertible and $A(\mathbf{x-y})=0$ then $\mathbf{x-y}=0$?
Jan
4
comment How to count the number of integer points in a polyhedral?
Not a complete answer, but picks theorem might help. Compute the area with some other method and use that to get the number of points.
Jan
1
asked Suppose $f:N \to N$ is increasing. Does there exist an $M$ such that $m=\sum_{i=1}^M f(a_i)$ always has a solution?
Dec
25
accepted How does the size of the set $A(R) = \{(a,b) \; | \; a,b \in N \times N, \; \gcd(a,b) = 1, \; a^2 + b^2 \leq R^2\}$ grow?
Dec
24
comment How does the size of the set $A(R) = \{(a,b) \; | \; a,b \in N \times N, \; \gcd(a,b) = 1, \; a^2 + b^2 \leq R^2\}$ grow?
I like this! Can you fill in some of the details between (4) and (5)?
Dec
24
comment How does the size of the set $A(R) = \{(a,b) \; | \; a,b \in N \times N, \; \gcd(a,b) = 1, \; a^2 + b^2 \leq R^2\}$ grow?
Yes, I'm interested in the leading term. Do you care to write an answer?
Dec
24
revised How does the size of the set $A(R) = \{(a,b) \; | \; a,b \in N \times N, \; \gcd(a,b) = 1, \; a^2 + b^2 \leq R^2\}$ grow?
added 381 characters in body
Dec
24
comment How does the size of the set $A(R) = \{(a,b) \; | \; a,b \in N \times N, \; \gcd(a,b) = 1, \; a^2 + b^2 \leq R^2\}$ grow?
@DanielFischer Good question! In other words, can we relate $A(R)$ to the Gauss circle problem, but in this case, I don't care about second order terms.
Dec
24
asked How does the size of the set $A(R) = \{(a,b) \; | \; a,b \in N \times N, \; \gcd(a,b) = 1, \; a^2 + b^2 \leq R^2\}$ grow?
Dec
24
comment $f(x+1)-f(x)$ converges $\Rightarrow\frac{f(x)}x$ converges
Intuitively, $f(x) = \sum f(n+1+x)-f(n+x) = (L+\epsilon) \lfloor x \rfloor +A(x)$ for some constant $A(x)$. $A(x)$ will be bounded since it will inherit some continuity from $f(x)$. With this you can see why we have convergence.
Dec
23
revised function such that $f(x\cdot t)=f(x)g(t)$
deleted 66 characters in body
Dec
23
comment function such that $f(x\cdot t)=f(x)g(t)$
@PedroM., you are correct. Silly error. Thanks!
Dec
23
answered function such that $f(x\cdot t)=f(x)g(t)$
Dec
23
accepted Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
Dec
23
comment Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
Alright, I get this! Very nice!
Dec
23
revised Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
added 180 characters in body
Dec
23
revised Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
edited tags
Dec
23
comment Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
I didn't think of generalized holder!