HP 50g Programming Competition: How Many Partitions of an Integer in 4 Squares

[c0manche]

(04-16-2018 11:31 PM)Valentin Albillo Wrote:  

(04-15-2018 08:36 AM)pier4r Wrote:  Nice observations Valentin and Gerald! (And Thomas of course).

Thanks for your appreciation and kind comment.

Quote:Can someone get 720^20-3 factorized at all (in a calculator context), and only after that factorized quickly? (Same for 720^20-18 and all the others hard variants)

I very much doubt it's doable on any 2018-era calculator (let alone "quickly") as 720^20-3 has two 23-digit prime factors and 720^20-18 has a 22-digit prime factor and a 35-digit one. In similar fashion, 720^20-19 and 720^20+19 are both prime.

Regards.
V.
.

No surprises here just tried factorising 720^20-3 on an HP Prime and it throws a quadratic sieve failure