MathDB

1

Part of 1982 Vietnam National Olympiad

Problems(2)

Roots of polynomial are cos 72 degrees and cos 144 degrees.

Source: Vietnam MO 1982 P1

3/17/2011
Determine a quadric polynomial with intergral coefficients whose roots are cos⁡72∘\cos 72^{\circ} and cos⁡144∘.\cos 144^{\circ}.
algebrapolynomialcalculusintegrationtrigonometryVietaalgebra proposed
number theory equation

Source: concurs 2003

7/10/2005
Find all positive integers x,y,zx, y, z such that 2x+2y+2z=23362^x + 2^y + 2^z = 2336.
number theory proposednumber theory