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Least value of n

Source: China TST 2006

June 18, 2006

algebrapolynomialnumber theorygreatest common divisormodular arithmeticvectorlinear algebra

Problem Statement

Let

a_{i}

and

b_{i}

(

i=1,2, \cdots, n

) be rational numbers such that for any real number

x

there is:

x^{2}+x+4=\sum_{i=1}^{n}(a_{i}x+b)^{2}

Find the least possible value of

n