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Oct
17
revised How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?
edited title
Oct
17
comment How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?
A non-pythagorean question is added.
Oct
17
revised How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?
added 79 characters in body
Oct
17
revised How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?
added 79 characters in body
Oct
17
comment How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?
Ah, $(a^2-b^2)^2+(2ab)^2=(a^2+b^2)^2$. So I have to find all $(a,b)$'s such that $a^2+b^2=2m$.
Oct
17
comment Solution to a system of linear equations in GF(2)
An insightful answer. It is brilliant to consider $A^2$. To solve the puzzle I have to handle all the cases so I give the "√" to @user1551, but this is impressive.
Oct
17
comment Solution to a system of linear equations in GF(2)
Thank you, @user1551. Actually the question is from a variant of lights out puzzle, where the light pressed affects the whole row and column.
Oct
17
asked How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?
Oct
17
accepted Solution to a system of linear equations in GF(2)
Oct
7
comment Solution to a system of linear equations in GF(2)
I can't see why the rows $1,n+1,\cdots,(m-1)n+1$ are identical. Take $A$ for an example: after manipulation, the 1st row is $(1,1,1,0,0,0)$ and the 4th row is $(1,0,0,1,1,1)$. Did I make some calculation mistakes?
Sep
25
revised Solution to a system of linear equations in GF(2)
added 104 characters in body
Sep
25
revised Solution to a system of linear equations in GF(2)
added 11 characters in body
Sep
25
revised Getting the inverse of a lower/upper triangular matrix
added 4 characters in body
Sep
25
accepted How to calculate dual frames under constraints?
Sep
25
asked Solution to a system of linear equations in GF(2)
Aug
28
comment infinite series of the form $\sum\limits_{k=1}^{\infty}\frac{1}{a^{k}+1}$
Not a proof but I've tried "Plot[NSum[1/(a^k + 1), {k, 1, [Infinity]}] - (-Log[a/(a - 1)] + QPolyGamma[0, 1 - (I [Pi])/Log[a], 1/a])/Log[a], {a, 2, 10}]" in Mathematica and it turns out to be a zero function.
Aug
19
awarded  Tumbleweed
Jul
20
comment Can anyone recommend some books on PDE in $L^p$ space for me?
@Jack: Oops... 18-155
Jul
13
answered How am I supposed to substitute these integral bounds?
Jun
26
revised How to use Galerkin method to prove uniqueness of solutions of hyperbolic equations?
uniqueness -> existence