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9:35 AM
1
Q: Prove e^x = (1+dx)^(x/dx)

Mahmud Nabil SnigdhoSorry for asking this freaky question. Is this kind of use of the differential x is valid? $$f(x)=e^x$$ $$\frac{d} {dx} \{f(x)\}=f(x)$$ $$d\{f(x)\}=f(x) dx$$ Now, $$f(x)=f(x-dx)+d\{f(x-dx)\}$$ $$=f(x-dx)+f(x-dx)dx$$ $$=f(x-dx)(1+dx)$$ $$=f(x-ndx)(1+dx)^n$$ $$=f(x-\frac{x}{dx}dx)(1+dx)^{\frac{x}{d...

Very shortcut method here
 
 
3 hours later…
12:41 PM
@Peter your gap calculation comes doen to this ... adding 2 to be prime makes it 5 mod 6 ( aka 11,17,23,29 mod 30) , adding 6 to be prime takes away 29 mod 30, and adding 24 ( aka -6) to be prime eliminates 11 mod 30.
going to 210 we have as a start 17, 23, 47, 53, 83, 107, 113, 137, 143, 167, 173, 197 mod 210 . This plus the adding 120 ( aka subtracting 90) must be prime rule limits to 17, 23, 47, 53, 107, 113, 137, 143, 173, 197 mod 210
and the 720 rule limits to 17, 23, 47, 53, 107, 137, 143, 173 mod 210
 
1:06 PM
[107, 1487, 1907, 3467, 4007, 4217, 5777, 6197, 7367, 8297, 8507, 9467, 9677, 11657, 13757, 13967, 15557, 17657, 17867, 19847, 20387, 21017, 21947, 22157, 23327, 24677, 25307, 25847, 27617, 29207] mod 30030 I believe...
hope that helps @Peter
 
1:26 PM
only 180 values mod 510510 that survive as posdibilities to 16!
@Steven31415 you aren't @MrPie are you ?
 
What?
 
last time I checked, I was not MrPie :)
 
oh xD
Steven 31415
 
2:34 PM
@Steven31415 do you know PARI GP
 
@RoddyMacPhee Yes, I know it!
I follow the developer's research on RG gate as well
got experience with it?
 
made a chatroom about it and learned part of what I know from an OEIS editor.
I'm not the usual use something for what it's for person though.
I may have helped speed it up by showing ways to get the same answer out of it.
if can be used to implement || , &&, !, and & , != can be implemented via subtraction mostly.
Vecrev(a) is equal to $vector(#a,i,#a-i+1)$ in effect
apply(s->2*s[1]+1,select(r->r[2]!=r[3]&& #select(q->r[2]==q[1]||r[3]==q[1],c[1..vecmax(r)\4])==0,c=setbinop((a,b)->[2*a*b+a+b,a,b],[1..100]))) poor semiprime sieve of factors up to limit

luhn(n)=my(a=Vecrev(digits(n)),b);a=vector(#a,i,if(lift(Mod(i,2))==1,vecsum(digits(2*a[i])),a[i]));b=concat(n,ceil(vecsum(a)/10)*10-vecsum(a)) most id numbers etc.

upc(n)=my(a=Vecrev(digits(n)),b);a=vector(#a,i,if(lift(Mod(i,2))==1,3*a[i],a[i]));b=concat(n,ceil(vecsum(a)/10)*10-vecsum(a)) or ISBN 13...

my(a=vector(100,i,random(100)));print(Pol(a));a=matrix(ceil(#a/eulerphi(100)),eulerphi(100),j,k,if(eule

 PARI/GP programming

For learning, teaching, and speeding up, PARI/GP programming, ...
 
3:00 PM
Are you involved in the development of it?
 
not really just found interesting things in it. or complained enough that it may have been sent to karim
anyways should try and get back to FOIL in mod lol
I still can't remember why mersenneforum wanted to nominate me for a fields medal at one point. Collatz, Goldbach etc. can all be restated in many ways.
 
3:37 PM
nice :D
 
4:10 PM
Is there a tag for computational stuff
Like running programs to check for solutions and stuff.
 
4:26 PM
solution verification is if you have a solution you want checked. probably hslf a dozen tags could fit in some way.
 
5:25 PM
$b\to 1\land _2|c|>d\implies cx+b\to 3^e{c\over 2^{_2|c|}}x+1$
 
5:50 PM
3
Q: The new year $2020$, as sums of squares

Manoj KumarIs it true that $2020$ is the smallest number that can be written as the sum of the squares of four consecutive primes and as the sum of $2$ squares in two ways? In this case, $$2020=17^{2}+19^{2}+23^{2}+29^{2}$$ $$2020=16^{2}+42^{2}$$ $$2020=24^{2}+38^{2}$$ I read this on the Twitter page of...

Lol XD
 
sorry that was a formulation about Collatz
 
6:33 PM
Would anyone like to write a sum of squares equal to another sum of squares, coefficients not bigger than 10, no more than five partial sums on each side?
 
$3^2+4^2+5^2=13^2+0^2+0^2$
doh $12^2$ not $5^2$
not hard. iterate pythagorean triples.
 
7:16 PM
Anything else @MrPie
 
7:38 PM
my(r=[1],s=2);forprime(p=3,7,r=fold(concat,vector(p,i,apply(q->q+(i-1)*s,r)));s=s*p;r=select(w->gcd(w,s)==1,r));r here help @Peter @MrPie
 
7:51 PM
modular multiplicative group representatives mod primorials if you're wondering
 
 
1 hour later…
9:21 PM
What are you working on @Mathphile ?
 
9:34 PM
nothing much just got back to uni
 
hopefully code helps your university
 

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