jackdean
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Member for 1 year, 4 months
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Last seen this week
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Is there a set of point $S \subset \mathbb R^2$ such that $|\{C: C \text{ is unit circle boundary }, |C \cap S| = 10\}| > |S|$
the solution is correct. the last part can be change to calculating the expected value from E(|circle has exactly 10 red point| - |red points|) > 0. very fascinating solution
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Is there a set of point $S \subset \mathbb R^2$ such that $|\{C: C \text{ is unit circle boundary }, |C \cap S| = 10\}| > |S|$
right, i forgot thank for correcting
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Elementary method for finding integer solutions for certain types of elliptic curve
Certainly! finding all fibonacci number which also square for example, it's equivalent to solve $5x^4+4=y^2$ and substitute into the integral solution of the curve $x(5x^2+4) = y^2$
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Elementary method for finding integer solutions for certain types of elliptic curve
sorry my mistake, $Q$ is a quadratic polynomial, if $z=x^2$ is a solution to $Q(x^2) = dy^2$ then $dz(Q(z))$ is also a perfect square, so just need to solve the later
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Elementary method for finding integer solutions for certain types of elliptic curve
added 6 characters in body
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"Make all numbers equal" game
you can look at other comments
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"Make all numbers equal" game
@EmilJeřábek the process of Joseph Van Name guaranteed that the all of them will eventually be $z$ times a power of $2$ this is useful since it can be generate by a pair of two $z$, Im not sure if there is a faster process to approach the same
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"Make all numbers equal" game
It's feel very surprising to me that the most steps-consuming part is making $2^t$ elements equal which take about $O(t2^t)$ steps.
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"Make all numbers equal" game
actually you only need $4 * (2b-a)/2$ steps to bring all the $z$ to $16z$
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"Make all numbers equal" game
correction number of moves
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"Make all numbers equal" game
I think optimizing the minimum steps to make the list equal largely rely on this case. Because you only need $O(nlog(n))$ step to standardize the list to the case where only 2 distinct elements. And in the next step (transfer real case down to integers) you will not want the output integer being too big. I guess the minimum number of step needed is indeed $O(nlog(n))$