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2011x^3 +ax^2 +bx+c = 0 if a+ b + c = 2010 \cdot 2011

Source: 2011 Saudi Arabia Pre-TST November 1.2

January 1, 2022
number theory

Problem Statement

Find all triples (a,b,c)(a, b, c) of integers such that a+b+c=2010ā‹…2011a+ b + c = 2010 \cdot 2011 and the solutions to the equation 2011x3+ax2+bx+c=02011x^3 +ax^2 +bx+c = 0 are all nonzero integers.
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