Spectre

Acha lagega muche.. (was my Hindi correct? I meant to say 'I'd feel good')

I wish I were a mathematician like you, bhai!

@RajdeepSindhu Overall... Maths I got a dirty 95... I did 10 questions and got 4 incorrect (I was a bit careless... plus I couldn't think of patiently trying the lengthy ones... I did the general strategy of doing physics and chemistry first (physics I did 15 and got 2 incorrect - carelessness there too! And chemistry I did 11 and got 5 incorrect, for the same reason)

@RajdeepSindhu my percentile: 93.3362866

I just came around while searching for some files.. bye anyway! :)

Guys, how was your JEE? My firsts ession itself kharab hai... gonna try the next session!

@Devansh Currently in grade 12

@Devansh Oh no, pal! How come I be in college when I haven't written JEE?? 😂 Nice question!

Anyway byee for now, hope everyone's good

Btw, how's everyone's prep for the boards and entrance going?? Mine is somewhat rugged, still tryna keep up

Heya pals!! Just dropped in while working on my CS project... hope none of you deemed me dead ':D

@Wolgwang No... oh my! I think I was mentioning it as if we had two projects a year! Sorry, it's just one

And yeah, all you need to follow is: do whatever that's possible for you to complete at least a week before the last date. The rest you can do as per how much time you can save for it, yet you must complete it in major chunks, thus reducing your load

Math we didn't perform the activity, but writing it up was still good

CS we did, I'm jolly happy about being able to do so

Physics we couldn't do

For English I feel lucky for having been able to know more about William Saroyan...

@LalitTolani If you're in grade 11, I'll you my case; in my case we're asked to write them down as given, with suitable dates as in the PDF and bundle them all up per subject. However, when it came to the chem project of term 2, my teacher asked us to try it if we could, to obtain data; else we were allowed to copy from friends. I wouldn't like this to go too public, but that's how it went

@LalitTolani They're unpredictable like accidents. You go riding in all joy and there comes a crash :D

@hansika True... that was a rash decision, it seems. I wouldn't like to see them shrink it to two attempts per individual for ever; but perhaps they might...

@AshishAhuja Me too, since one can get chances to improve and time to reinforce information that one is likely to forget into his/her brain

@Arjun Better say "Hi: Reloaded" lol... as if we were playing with film names! xD

Anyway byee

"So I thought the meaning of "your girl" should be what one must find first, so I put up my thought" - then I added not to go in search that girl since we're not sure of she's ever got an Aadhar

@Prithubiswas He's da culprit then :D

So I thought the meaning of "your girl" should be what one must find first, so I put up my thought

You asked what the meaning of the sentence was

@Prithubiswas Well, just a joke

So if you were to try and find the least positive integer value for $ax + by, (a,b) = 1$ and you had no idea about Bezout's identity, you might try to do it as an optimisation problem and yet obtain the same results.

@Koro I asked him about that; I just mentioned the other question stating how stupid I seem at times :D

@Koro The question I mentioned is the one in the third edited comment in the comment block before your reply

I think that itself is a consequence of Bezout's identity with a pair of coprime integers (here, $2$ and $1$)

@Koro Btw I tried doing the sort of random testing in Bezout's identity with $a = 6, b =3$. As we know, $g = (a,b) = 3$; also we're interested in finding the least positive integer value of $6x + 3y$. Now suppose that there was an element smaller than the GCD that is positive. We can write the inequality $0 < 6x + 3y < 3 \implies 0 < 2x + y < 1$. We see, there can't be an integer between $0$ and $1$, hence the least possible value of the expression must be $3$.

@Koro Who would ask it unless the person is a beginner or a university student seeing Number Theory in its most beautiful form for the first time?

Byee then

At first I felt something was off with the question since there are a lot of unknowns, the solution (if at all there was one) would be a lot exhaustive, or if it never existed, still lives in a mathematician's library as an unsolved problem

@Koro do you have any idea about this question?

And I saw that the backlashes might begin once I saw the single downvote, so I deleted my answer and left the problem for good 😂

The second part was where I was a but flawed; I tried to write a proof as if to explain the phenomenon but in vain, so I left it as a partial answer

I put up an answer that at first talked about correcting the question to make the procedure work properly, since when $2$ is taken for $p$ or $q$, contradictions can arise

What the OP needed to know was the reason for this to happen (and something else as well, I had forgotten it)

It is seen that $k$ will have only two prime factors

So let $k = \frac{x}{2^{v_2(x)}}$

Now we see that $x$ will have powers of $2$ in the prime factorisation (I had forgotten to mention that $p$ and $q$ are both odd)

The define another number $x = Z - n$

Now define $Z = LH$

(Consider a number $N=pq,p,q∈\mathbb{P}$ ($\mathbb{P}$ being the set of primes) - now define $H$ as the closest prime to $N$ that is greater than $N$, $L$ defined the same way but less than $N$.

To connect the chain of logic is what's giving me a lil bit of confusion

But that isn't what's giving me the trouble

@Koro I understood using that should help one round in upon an element in the set $S = \lbrace ax + by : ax + by > 0, x, y \in \mathbb{Z} \rbrace$