Infinitely many solutions (a,b,c)
Source: Moldova NMO 2002 grade 7 problem nr.8
October 31, 2008
Problem Statement
Prove that there are infinitely many triplets that satisfy the following equalities:
\dfrac{2a\minus{}b\plus{}6}{4a\plus{}c\plus{}2}\equal{}\dfrac{b\minus{}2c}{a\minus{}c}\equal{}\dfrac{2a\plus{}b\plus{}2c\minus{}2}{6a\plus{}2c\minus{}2}