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13m
comment $6^{66}\equiv r \pmod {66}$
Alternatively $6^n \equiv 6^{n+10k} \bmod 66$ for positive integer $n$ so $6^{66} = 6^{6+10 \times 6} \equiv 6^6 \equiv 60 \bmod 66$
20m
answered $6^{66}\equiv r \pmod {66}$
25m
comment Computing irrational numbers
Different problems often require different methods.
34m
comment Working out a sequence from later terms
Just for comparison with Atvin's and abel's initial answers of $699$ and $697$, I think the $100$th term is $599$. Now they do too.
37m
comment Working out a sequence from later terms
Your $a_{100}=699$ looks too high to me
41m
answered Working out a sequence from later terms
1h
comment Random Variables and Moment Generating functions
You are using a symbol $􏰂$ that my computer cannot read
1h
answered Equation for sinusoidal wave with fixed wavelength and amplitude
1h
comment Equation for sinusoidal wave with fixed wavelength and amplitude
y = a * sin( x * 2 * pi / w ) ?
19h
comment Bivariate Normal Distribution Problem vs Marginals
$X_2$ is not normally distributed in terms of its marginal distribution. So $X_1,X_2$ cannot have a bivariate normal distribution But, given $X_1$, it is true that $X_2$ is conditionally normally distributed. I illustrated the chart using R, but you should have been able to sketch it yourself.
22h
answered Bivariate Normal Distribution Problem vs Marginals
22h
comment A not very easy problem…
You might try showing the first few terms of the Taylor expansions, at least up to $x^4$
22h
comment A not very easy problem…
A more descriptive title might help too
1d
comment Maximum $C$ such that every shape in $\Bbb R^2$ with area $<C$ can be placed to avoid $\Bbb Z^2$
related: math.stackexchange.com/questions/1290823/…
1d
comment Prove that there is a real number $a$ such that $\frac{1}{3} \leq \{ a^n \} \leq \frac{2}{3}$ for all $n=1,2,3,…$
It seems unlikely. Even with $\phi \approx 1.618$ you have $\phi^2=\phi+1$ but it breaks down for $\phi^3 \approx 4.236$
1d
comment What is the probability that on a given day, the number of half gallon containers provided is enough?
The central limit theorem with a continuity correction will probably give a reasonable approximation
1d
comment Three points on a circle
You could extend this argument to the probability of $n$ random points lying in a circular segment with angle $\phi \le \pi$, to give a probability of $$n\left(\dfrac{\phi}{2\pi}\right)^{n-1}.$$ I suspect the position is harder for $\pi \lt \phi \lt 2\pi \frac{n-1}{n}$.
1d
comment Four points inside a rectangle
Do you draw the halves after you see the points? What makes a half (e.g. any straight line through the central point)?
2d
comment A CD players plays songs until a certain artist is selected.
(a) looks correct. (b) looks wrong and I would have thought was easier than (a)
2d
comment A CD players plays songs until a certain artist is selected.
(c) looks in conflict with "It will repeat this process until it picks a song from artist B. At which point it will turn off."