Quadratic Sieve: How to find the first number divisible by the element from the Factor Base?

The number to be factored is $N$.


  • Create the factor base. Let it be List $FB = {p1, p2, p3, p4, …}$

  • Generate a list which needs to be sieved down. Let this be List $L = {x1, x2, x3, x4….}$

  • The quadratic polynomial we are using is $f(x) = x^2 – N$
    It’s trivially proved that if $f(x) pmod p1 equiv 0$, then $f(x + kp1) pmod p1 equiv 0$

  • Starting with $p1$, solve $x^2 – N equiv 0 pmod p1$

  • If we find a number(root) $x0$ as the solution of the above, then it’s divisible by $p1$ & $(x0+p1, x0+2p1, x0+3p1..)$ are also divisible by $p1$. So we can sieve the List L using this.

I understood up to this much.

However, once we reach this stage, how does one find the first number in List $L$ which is divisible by $p1$? Do we need to go trying $x1, x2, x3$ etc by trial division till we find the first one divisible by $p1$? Once I find it, then other numbers like $x1 + p1, x1 + 2p2$ etc can easily be found without further division.

However, is going through the List $L$ by trial division the way to find the first one or is there a better way which I am missing?

Find if widget block is active

I’m used to check if a widget from installed my plugin is active.

With the new block editor extending to widgets in WordPress 5.8, I was wondering if there is a way to check the widget block that I created (both old php-based and gutenberg-based widgets are installed by my plugin) is activated by the user.


How to find basis [w]?

Find (w)b and (w)b with respect to the basis B = {v1, v2}
for R^(2).

w = (3,7); v1 = (1,0), v2 = (0,1)

The answer is w(3,7) but i don’t understand?

How to find a quality package home moving service in Dubai?

How to find a quality package home moving service in Dubai? I really need help with this, since this is the first time I’m moving to another country for a long time.


Why You Don’t Find Japanese People Online

Why is there a lack of Japanese people online?

Another example of why you should ask if before you ask why.

There are millions of Japanese people online. Go onto Instagram and start typing in something like 可愛い into the search bar, and I can guarantee you’ll find thousands, if not millions of posts in the hashtag. If basic Japanese is beyond your abilities, try typing in a location on there. Sure, you might have to sift through a few more profiles, but you’ll find a good share of Japanese there.

Questions like these make it pretty clear that the OP probably meant to ask “why don’t I see a lot of Japanese people in my feed?” instead.

The answer is simple; if you don’t read and write Japanese, you’re not going to find very many Japanese in your feed. Most Japanese people only are literate in Japanese, in the same way most Americans can only write in English.

And besides, when was the last time you went out of your way to post your stuff out there and interact with people from other countries, in languages that you can’t speak? If you can’t think of anything, I can’t imagine why it would be hard to understand that the average Japanese wouldn’t be much different in that regard.

Another answer:

Maybe because you can’t read and write Japanese.

Japan’s official language is Japanese and their mother tongue is Japanese. Japan has the 10th largest population in the world and they have wide range of hobbies, interests, topics, and other users to communicate about/with within Japanese community. Except for very few who are particularly interested in English, they wouldn’t be visible to you.

If you know how to search in Japanese, you would find tens of millions of Japanese people on social media.

Source: https://www.quora.com/Why-is-there-a-lack-o…e-people-online

Profits from games of knowledge: https://www.predictmag.com/

probability – If $f(y)=(1— theta)+2theta y,$ find an estimator of $theta$ by Maximum likelihood estimation.

The random variable $Y$ has a probability density function

$f(y)=(1— theta)+2theta y,$ for $0 <y< 1$

for $-1 < theta < 1$. There are $n$ observations $y_i. i = 1,2,…,n$, drawn independently from this distribution. Derive the Maximum Likelihood Estimator of $theta$.

I have tried to differentiate the log likelihood function. But I am stuck at that step. I am not sure how to find an expression for the estimator. Any help would be highly appreciated.

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dnd 5e – Find familiar spell, Sanctuary, and spell attacks in DnD 5th edition

Both castings of sanctuary end.

Sanctuary states:

If the warded creature makes an attack, casts a spell that affects an enemy, or deals damage to another creature, this spell ends.

Since you are casting inflict wounds which goes on to affect an enemy, sanctuary ends for you. Find familiar states:

Finally, when you cast a spell with a range of touch, your familiar can deliver the spell as if it had cast the spell. Your familiar must be within 100 feet of you, and it must use its reaction to deliver the spell when you cast it. If the spell requires an attack roll, you use your attack modifier for the roll.

Now, your familiar delivers the spell as if it had cast it. This indicates that the familiar is making the attack for inflict wounds. If the familiar had cast inflict wounds it would deliver it by making an attack against the target, ergo it makes an attack when you cast the spell through the familiar. Therefore, sanctuary ends for the familiar as well.

It is worth mentioning that this does create an odd situation that might cause a DM to rule that sanctuary does not end for the caster of inflict wounds. If the familiar’s attack misses, one might argue that the inflict wounds spell did not affect the enemy creature, and so sanctuary would not end for the caster. I wouldn’t rule this way, but there is room for it.

Find familiar spell, Sanctuary, and spell attacks

So find familiar spell lets you cast touch-ranged spell, and sanctuary states that it ends when the warded creature makes attack (not possible) cast a spell that affects an enemy (not their spells, but mine), or deal damage to other creature (again it’s my spell, charged towards it). If both me and my familiar has sanctuary on, and i want to cast inflict wounds using my familiar, which of the 2 sanctuary would have ended?

Find smallest instance satisfying certain inequalities

I need a "clean" way to find the smallest solution to some (in)equalities given by Reduce and containing only one variable x. For example, such an expression could be 1 ≤ x ≤ 2, x == 9 or -1 ≤ x ≤ 4 || 7 ≤ x ≤ 11 || x == 5. I know that FindInstance finds some instance, but I don’t know how to restrict the search to the smallest one (it outputs {{x -> 43/34}}, {{x -> 9}} and {{x -> 2/7}} for the previous examples).

In principle, this could be done by using patterns to extract the endpoints of the intervals and choosing the smallest one, but I think there should be a cleaner way.