MathDB

1

Part of 1985 IberoAmerican

Problems(2)

1st ibmo - colombia 1985./q1

Source: Spanish Communities

4/6/2006
Find all the triples of integers (a,b,c) (a, b,c) such that: \begin{array}{ccc}a\plus{}b\plus{}c &\equal{}& 24\\ a^{2}\plus{}b^{2}\plus{}c^{2}&\equal{}& 210\\ abc &\equal{}& 440\end{array}
ColumbiaalgebrapolynomialVietamodular arithmeticsymmetryalgebra unsolved
1st ibmo - colombia 1985./q4

Source: Spanish Communities

4/6/2006
If x≠1 x\neq1, y≠1 y\neq1, x≠y x\neq y and \frac{yz\minus{}x^{2}}{1\minus{}x}\equal{}\frac{xz\minus{}y^{2}}{1\minus{}y} show that both fractions are equal to x\plus{}y\plus{}z.
Columbiaalgebra unsolvedalgebra