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ax + by + cz + dw ≡ 1 (mod p)
ex + fy + gz + hw ≡ 1 (mod p)
(p is prime, 0 <= a,b,c,d,e,f,g,h < p, 0 <= x,y,z,w < p, all varients are integer)
I only know the values of a, b, c, d, e, f, g, h, and I have to get x, y, z, w.
How can I solve this using computer? I have no idea 🙁
These are just standard linear equations in the field of integers modulo p.
So you can use Gauss elimination.
The only thing that is a little bit tricky is to compute the inverses.