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enzocreti 2020-04-04 11:47

Is this fact provable?
 
I asked it on mathexchange but I did not receive a clear answer.


Consider this Pari code:

liste(lim,mul,base=34,step=5590,offset=588)=my(v=List(),X=mul*base); lim\=1; while(X<lim,forstep(n=X+offset+step,lim,step, listput(v,n)); X*=base); Set(v)
list(lim)=setunion(liste(lim,23),liste(lim,223))
v=list(1e6)

This code generates numbers: if I am not wrong numbers generated by that Pari code which are multiple of 43 are also congruent either to 0 or 344 mod 559. Is this true and why?
:
liste(lim,mul,base=34,step=5590,offset=588)=my(v=List(),X=mul*base); lim\=1; while(X<lim,forstep(n=X+offset+step,lim,step, listput(v,n)); X*=base); Set(v)
list(lim)=setunion(liste(lim,23),liste(lim,223))
v=list(1e6)


If you add this Pari code
subset1 = select((x) -> (x % 43 == 0), v);
subset2 = select((x) -> (x % 43 == 0) && (x % 559 == 0 || x % 559 == 344), v);
vecsort(subset1) == vecsort(subset2)
> 1

you should test that actually numbers 0 mod 43 are either 344 or 0 mod 559


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