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Jan
4
accepted Solving an inequality modulo 1
Nov
19
comment Deriving time and distance
$\frac{d}{dt}D$ is in meters per second, but your speed is in kilometers per hour.
May
13
awarded  Caucus
May
11
awarded  Critic
Apr
18
answered Finding a position opposite to a rotated point
May
2
suggested suggested edit on Adjacent sequences example
May
2
comment Solving an inequality modulo 1
Ah, that makes sense. I'll definitely try to see what I can do with this.
May
2
comment Solving an inequality modulo 1
Thank you for the detailed answer, I really appreciate it. Is there any reason you chose $3$ and $2$ for the bounds in this expression: $\frac{n}3<i<\frac{n}2$? The reason why I'm looking for an analytic solution for $i$ is because I'm trying to factor a large number, just to see how efficiently I can do it. Each of the possible $i$'s corresponds to a possible factor of a number $n$. I've found graphically that these $i$'s grow very predictably for arbitrary $n$, as you can see in this graph I tried to make (each peaks correspond to an $i$).
May
2
comment Solving an inequality modulo 1
I guess you're right. Thanks for the help!
May
2
comment Solving an inequality modulo 1
I'm basically trying to factor a number with only two prime factors. If you look at the value of the function for $i$ ranging from $0$ to $\sqrt{n}$, you can see that the distance between the peaks of the function is growing predictably. Instead of trying to factor the number by trying every possible factor, I thought it might be a bit faster to try only the factors that correspond to the peaks, as the set of all prime factors of the number will exist within the solution set of the inequality I posted in my question. Hopefully that makes at least some sense.
May
2
comment Solving an inequality modulo 1
The code that I have works exactly the same was as you have described, but I'm trying to find a way to analytically solve for $i$ or at least make the solution easier to calculate.
May
2
comment Solving an inequality modulo 1
@Kaz: Right, I'm only worrying about the fractional part of the real number. $i$ will always be smaller than $\sqrt{n}$.
May
2
revised Solving an inequality modulo 1
added 7 characters in body
May
2
comment Solving an inequality modulo 1
@BrettFrankel: Ah, my bad. Thanks for the clarification.
May
2
revised Solving an inequality modulo 1
added 17 characters in body
May
2
comment Solving an inequality modulo 1
@BrettFrankel: I'm not entirely sure about notation for inequalities involving the modulo operator, but I think this makes a bit more sense: $\frac{n}{i}\text{ (mod 1) } < \frac{n}{i + 1}\text{ (mod 1) for } n, i\in\mathbb{N}$
May
2
comment Solving an inequality modulo 1
@BrianM.Scott: Yes, that's exactly what I'm trying to do.
May
2
asked Solving an inequality modulo 1
Dec
5
awarded  Yearling
Sep
20
comment How to find the function $f$ given $f(f(x)) = 2x$?
I've updated the answer. @Asaf, would saying that $f(f(-x)) = -f(f(x))$ be enough to prove that $f(x)$ is invertible?