Question

Arata ca numarul este patrat perfect:
x(x+1)(x+2)(x+3)+1, x apartine lui Z

Answer 1

x(x+1)(x+2)(x+3)+1 = $(x^{2} + x)(x+2)(x+3)+1 = \\ = (x^{3} + 2x^{2} + x^{2} + 2x)(x + 3) + 1 = \\ =(x^{4} + 2x^{3} + x^{3} + 2x^{2} + 3x^{3} + 6x^{2} + 3x^{2} + 6x) + 1$