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Jun
13
asked Using Fermat's Little Theorem, find the least positive residue of $3^{999999999}\mod 7$
May
28
revised If $x\equiv y \pmod{\gcd(a,b)}$, show that there is a unique $z\pmod{\text{lcm}(a,b)}$ with $z\equiv x\pmod a$ and $z\equiv y\pmod b$
edited title
May
28
asked If $x\equiv y \pmod{\gcd(a,b)}$, show that there is a unique $z\pmod{\text{lcm}(a,b)}$ with $z\equiv x\pmod a$ and $z\equiv y\pmod b$
May
28
asked Prove that if $p_1,\dots,p_k$ are distinct odd primes then 1 has $2^k$ square roots $\mod m$ where $m$ is the product of the primes.
May
23
comment Prove that if $n\geq\text{lcm}(a,b)$ and $\gcd(a,b)|n$ then $n=xa+yb$ for some integers $x,y\geq 0$
I'm still rather stuck. I can't quite see how I can show that the coefficients are nonnegative from that. Can you possibly offer any other insight?
May
23
asked Prove that if $n\geq\text{lcm}(a,b)$ and $\gcd(a,b)|n$ then $n=xa+yb$ for some integers $x,y\geq 0$
May
17
awarded  Nice Question
Apr
22
accepted Is a broken clock right twice a day?
Apr
22
comment Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
I know this is an ancient thread but hopefully you're still lurking out there somewhere. How come you need to hope that $\lambda\ne 0$? Doesn't the argument still work just fine in the case where $\lambda=0$?
Apr
22
comment Is there a nice way to interpret this matrix equation that comes up in the context of least squares
@Dolma thanks I fixed that
Apr
22
revised Is there a nice way to interpret this matrix equation that comes up in the context of least squares
deleted 8 characters in body
Apr
21
asked Is there a nice way to interpret this matrix equation that comes up in the context of least squares
Apr
19
accepted Proving that if $f_n \rightarrow f$ uniformly and $f_n$ is integrable then $\int_a^b f_n d\alpha\rightarrow \int_a^b fd\alpha$
Apr
19
comment Proving that if $f_n \rightarrow f$ uniformly and $f_n$ is integrable then $\int_a^b f_n d\alpha\rightarrow \int_a^b fd\alpha$
almost want to delete this question in shame.
Apr
19
comment Proving that if $f_n \rightarrow f$ uniformly and $f_n$ is integrable then $\int_a^b f_n d\alpha\rightarrow \int_a^b fd\alpha$
oh my god......
Apr
19
asked Proving that if $f_n \rightarrow f$ uniformly and $f_n$ is integrable then $\int_a^b f_n d\alpha\rightarrow \int_a^b fd\alpha$
Apr
16
accepted Why do we need $A$ to have linearly independent columns in order for $P_A=A(A^TA)^{-1}A^T$ to hold?
Apr
16
comment Why do we need $A$ to have linearly independent columns in order for $P_A=A(A^TA)^{-1}A^T$ to hold?
@Suugaku No I know, I just don't know why it has to be a basis
Apr
16
asked Why do we need $A$ to have linearly independent columns in order for $P_A=A(A^TA)^{-1}A^T$ to hold?
Apr
5
comment Prove that if $\sum c_n e^{inx}$ converges in $L^2$ to $f$ then $c_n$ are the Fourier coefficients.
I don't see how you got the very first step. How are you able to say that $c_n$ is equal to that? Where, for instance, does the $\frac{1}{2\pi}$ come from?