Hp Algorithm to create random numbers

[Albert Chan]

(08-25-2024 02:50 PM)Albert Chan Wrote:  state * 2851130928467 ≡ 163041130928467 (mod 10^15)

Faster way to solve, scale to reduce multiplier to 1, 2nd column is state.

Cas> m := 10^15
Cas> [2851130928467, 163041130928467] * 3; /* force multiplier last digit = 1 */

[8553392785401,489123392785401]

Cas> (Ans*(2-Ans[1])) MOD m

[667229546840001,469799546840001]
[246014400000001,248584400000001]
[1,2570000000001]

--> state = 002570000000001

This trick work for other modulus too. Also, MOD can be signed mod

Example: solve 7x ≡ 9 (mod 3^5)
Base 3, last digit 7%3 = 1, we keep scaling to zeroed out other digits.

Cas> [7, 9] %% 3^5
Cas> Ans*(2-Ans[1])
[-35 %% 243,-45 %% 243]
[-80 %% 243,36 %% 243]
[1 %% 243,36 %% 243]

--> x ≡ 9/7 ≡ 36 (mod 3^5)