modular sqrt does not always detect and error on non-prime modulus

[email protected] Tue, 28 Apr 2026 08:45:58 +0200
Newsgroups gmane.comp.mathematics.pari.devel
Message-ID <[email protected]>
Seems to be a little bug.
I found another factor than 3 that worked but not able to reproduce now.
Not all primes of the form 1+k^2 behave wrong as k=6 shows:

? version
[2, 17, 3]
? sqrt(Mod(-1-2^2,3*5))
Mod(5, 15)
? sqrt(Mod(-1-2^4,3*17))
Mod(17, 51)
? sqrt(Mod(-1-10^2,3*101))
Mod(101, 303)
? sqrt(Mod(-1-2^6,3*37))
   ***   at top-level: sqrt(Mod(-1-2^6,3*37))
   ***                 ^----------------------
   *** sqrt: not a prime number in sqrt [modulus]: 111.
   ***   Break loop: type 'break' to go back to GP prompt
break>


Regards,

Hermann.