Question 147
Determine the smallest positive integer $n$ for which there exist integers $a_1, a_2, \dots, a_n$ such that the polynomial
$$x^2 - 2(a_1 + a_2 + \dots + a_n)^2 x + (a_1^4 + a_2^4 + \dots + a_n^4 + 1)$$
has at least one integer root. (P. Kozlov)
$$x^2 - 2(a_1 + a_2 + \dots + a_n)^2 x + (a_1^4 + a_2^4 + \dots + a_n^4 + 1)$$
has at least one integer root. (P. Kozlov)