MathDB

1

Part of 1987 Iran MO (2nd round)

Problems(2)

System of Equations - [Iran Second Round 1987]

Source:

12/8/2010
Solve the following system of equations in positive integers {a3−b3−c3=3abca2=2(b+c)\left\{\begin{array}{cc}a^3-b^3-c^3=3abc\\ \\ a^2=2(b+c)\end{array}\right.
algebrasystem of equationsnumber theory proposednumber theory
Calculate the product of sines - [Iran Second Round 1987]

Source:

12/23/2010
Calculate the product: A=sin⁡1∘×sin⁡2∘×sin⁡3∘×⋯×sin⁡89∘A=\sin 1^\circ \times \sin 2^\circ \times \sin 3^\circ \times \cdots \times \sin 89^\circ
trigonometryalgebra proposedalgebra