hermann on Fri, 06 Oct 2023 10:20:40 +0200


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Re: efficient foursquare() and/or threesquare1m4() functions 

On 2023-10-06 01:06, hermann@stamm-wilbrandt.de wrote:
Any ideas for efficient foursquare() and/or threesquare1m4() are welcome. 
I want to apply to these unfactored RSA-numbers =1 (mod 4):

$ gp -q RSA_numbers_factored.gp
? foreach(RSA.unfactored(1),r,[l,n]=r;print1(l," "))
280 309 310 320 340 360 370 390 400 430 450 460 1536 470 500 617 2048
?


I found an English talk outlining proof of the three square theorem:
https://warwick.ac.uk/fac/sci/maths/people/staff/michaud/threesquarestalk.pdf
After a first quick pass over the 28 slides, ternary quadratic forms seem to 
allow for an algorithm ...

PARI/GP user's guide has 41 hits for "quadratic form".
And one hit for "ternary quadratic form".


Regards,

Hermann.