Untitled (1)

> f:=x^3-x+1 ; discrim(f,x);

f := x^3-x+1

-23

> for i from 1 to 20 do print(ithprime(i), Factor(f) mod ithprime(i)) od ;

2, x^3+x+1

3, x^3+2*x+1

5, (x^2+3*x+3)*(x+2)

7, (x+5)*(x^2+2*x+3)

11, (x^2+5*x+2)*(x+6)

13, x^3+12*x+1

17, (x+5)*(x^2+12*x+7)

19, (x^2+13*x+16)*(x+6)

23, (x+3)*(x+10)^2

29, x^3+28*x+1

31, x^3+30*x+1

37, (x+13)*(x^2+24*x+20)

41, x^3+40*x+1

43, (x+10)*(x^2+33*x+13)

47, x^3+46*x+1

53, (x+37)*(x^2+16*x+43)

59, (x+42)*(x+4)*(x+13)

61, (x+57)*(x^2+4*x+15)

67, (x+7)*(x^2+60*x+48)

71, x^3+70*x+1

> f:=simplify((x^5-1)/(x-1)); discrim(f,x);

f := x^4+x^3+x^2+x+1

125

> for i from 1 to 20 do print(ithprime(i), Factor(f) mod ithprime(i)) od;

2, x^4+x^3+x^2+x+1

3, x^4+x^3+x^2+x+1

5, (x+4)^4

7, x^4+x^3+x^2+x+1

11, (x+7)*(x+2)*(x+8)*(x+6)

13, x^4+x^3+x^2+x+1

17, x^4+x^3+x^2+x+1

19, (x^2+5*x+1)*(x^2+15*x+1)

23, x^4+x^3+x^2+x+1

29, (x^2+6*x+1)*(x^2+24*x+1)

31, (x+29)*(x+23)*(x+27)*(x+15)

37, x^4+x^3+x^2+x+1

41, (x+25)*(x+4)*(x+23)*(x+31)

43, x^4+x^3+x^2+x+1

47, x^4+x^3+x^2+x+1

53, x^4+x^3+x^2+x+1

59, (x^2+26*x+1)*(x^2+34*x+1)

61, (x+3)*(x+41)*(x+27)*(x+52)

67, x^4+x^3+x^2+x+1

71, (x+46)*(x+17)*(x+14)*(x+66)

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