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Part of 2007 Irish Math Olympiad
Problems(2)
prime numbers
Source: Ireland 2007
7/6/2009
Find all prime numbers and such that divides q\plus{}6 and divides p\plus{}6.
number theory proposednumber theory
polynomial
Source: Ireland 2007
7/6/2009
Let and be the roots of the cubic polynomial: p(x)\equal{}x^3\minus{}2007x\plus{}2002.
Determine the value of: \frac{r\minus{}1}{r\plus{}1}\plus{}\frac{s\minus{}1}{s\plus{}1}\plus{}\frac{t\minus{}1}{t\plus{}1}.
algebrapolynomialVietaalgebra unsolved