it seems just because t2 is composite. 

Justin C. Walker於 2020年5月7日星期四 UTC+8上午4時34分22秒寫道:
>
>
>
> > On May 6, 2020, at 12:42 , Taylor Huang <asd0001...@gmail.com 
> <javascript:>> wrote: 
> > 
> > for copying convenience, 
> t2=1309093727683013566817782825108625009747446954546358949698232965571021678022482795164257607242612437837777327711946435277119464351117309193681
>  
>
>
> This may be more feature than bug.  If you break up the latter computation 
> (below), like 
>  t3 = mod(-1,t2)    # mod(-1,x) returns x-1 
>  t3.sqrt() 
>
> you get a response quickly, but it may not be what you are after. 
>
> t3 is 16*t4 
>
> but t4 is not prime, and is square-free (I believe Sage implicitly :-}). 
>
> Trying to factor it seems interminable (i.e., it hasn’t completed in ~5 
> minutes on my new iMac).  It may well be beyond the software’s attention 
> span, hence the message you got. 
>
> HTH 
>
> Justin 
>
> > 
> > Taylor Huang於 2020年5月7日星期四 UTC+8上午3時37分12秒寫道: 
> > As the attachment shown. kronecker(-1,t2) returns 1, but 
> mod(-1,t2).sqrt() says the square root cannot be done. 
> > It seems to be a bug. 
>
> -- 
> Justin C. Walker, Curmudgeon at Large 
> Institute for the Absorption of Federal Funds 
> ----------- 
> Like the ski resort full of girls hunting for husbands 
> and husbands hunting for girls, the situation is not 
> as symmetrical as it might seem. 
>   - Alan MacKay 
> -- 
>
>

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