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IMO LongList 1967, Romania 5

Source: IMO LongList 1967, Romania 5

December 16, 2004
trigonometryalgebrasystem of equationsTrigonometric EquationsIMO ShortlistIMO Longlist

Problem Statement

If x,y,zx,y,z are real numbers satisfying relations x+y+z = 1   \textrm{and}   \arctan x + \arctan y + \arctan z = \frac{\pi}{4}, prove that x2n+1+y2n+1+z2n+1=1x^{2n+1} + y^{2n+1} + z^{2n+1} = 1 holds for all positive integers nn.
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