Problem C. 857. (May 2006)
C. 857. Find the pairs (c,d) for which the equation x3-8x2+cx+d=0 has three (not necessarily) different positive integer roots.
(5 pont)
Deadline expired on June 15, 2006.
Sorry, the solution is available only in Hungarian. Google translation
Megoldás: Az gyöktényezős alakból kapjuk, hogy x1+x2+x3=8.
Az egyenlet megoldás számhármasai: (1,1,6); (1,2,5); (1,3,4); (2,2,4); (2,3,3).
Vagyis a megoldások: (13,-6); (17,-10); (19,-12); (20,-16); (21,-18).
Statistics:
117 students sent a solution. 5 points: 96 students. 4 points: 10 students. 3 points: 2 students. 0 point: 8 students. Unfair, not evaluated: 1 solutions.
Problems in Mathematics of KöMaL, May 2006