Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 472. (January 2009)

A. 472. Call a finite sequence (p1(x),...,pk(x)) of polynomials with integer coefficients Euclidean if there exist polynomials with integer coefficients such that d(x)=q1(x)p1(x)+...+qk(x)pk(x) is a common divisor of p1(x),...,pk(x), i.e. there are polynomials with integer coefficients for which pi(x)=ri(x)d(x) for every 1ik. Prove that whenever are polynomials with integer coefficients and every two of them form a Euclidean pair, then the sequence is Euclidean as well.

(5 pont)

Deadline expired on February 16, 2009.

### Statistics:

 3 students sent a solution. 5 points: Backhausz Tibor, Nagy 235 János, Tomon István.

Problems in Mathematics of KöMaL, January 2009