MathDB
2017 COMC B4

Source:

October 12, 2018
Comc2017 COMC

Problem Statement

Source: 2017 Canadian Open Math Challenge, Problem B4 —-- Numbers aa, bb and cc form an arithmetic sequence if b−a=c−bb - a = c - b. Let aa, bb, cc be positive integers forming an arithmetic sequence with a<b<ca < b < c. Let f(x)=ax2+bx+cf(x) = ax2 + bx + c. Two distinct real numbers rr and ss satisfy f(r)=sf(r) = s and f(s)=rf(s) = r. If rs=2017rs = 2017, determine the smallest possible value of aa.
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