在线等初等数论题x^3+4x^2+19x+1≡0(mod25)

因为x^3+4x^2+19x+1≡0(mod25)所以x^3-x^2+5x^2-5x+24x-24+25≡0(mod25)所以(x^2+5x+24)(x-1)≡0(mod25)而x^2+5x+24≡x^2-1≡(x+1)(x-1)(mod 5)所以①当x≡1(mod 5)时,5|x^2+5x+24且5|x-1,因此(x^2+5x+24)(x-1)≡0(m...