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116

Part of 1975 Chisinau City MO

Problems(1)

Chisinau MO p116 1975 R2 X xsin a+ysin b+z sin c=0 only 1 integer solution

Source:

3/16/2021
The sides of a triangle are equal to 2,3,4\sqrt2, \sqrt3, \sqrt4 and its angles are α,β,γ\alpha, \beta, \gamma, respectively. Prove that the equation xsin⁡α+ysin⁡β+zsin⁡γ=0x\sin \alpha + y\sin \beta + z\sin \gamma = 0 has exactly one solution in integers x,y,zx, y, z.
trigonometrynumber theoryradical