: This classic collection contains 320 unconventional problems in algebra, number theory, and trigonometry, originally used in the Moscow State University competitions. It is available as a verified PDF archive at Archive.org Art of Problem Solving (AoPS) Archive
Compare (3) and (4): set ( x y + f(x) = f(x) f(y) + x ) ⇒ rearr: ( (x-1)(y - f(x)) = 0 ) for all ( x,y ) — impossible unless ( x=1 ) always. So my step is flawed — known correct solution: after deducing ( f ) bijective and ( f(f(x))=x ), set ( y = f(t) ) in original ⇒ ( f(x t + f(x)) = f(t) f(x) + x ). Swap ( x ) and ( t ): ( f(t x + f(t)) = f(x) f(t) + t ). Subtract: ( f(xt + f(x)) - f(xt + f(t)) = x - t ). russian math olympiad problems and solutions pdf verified
: The Art of Problem Solving (AoPS) hosts a comprehensive user-verified archive of the All-Russian Olympiad. You can find organized PDF collections for specific years, such as the 2019 All-Russian Olympiad and the 2021 All-Russian Olympiad . Swap ( x ) and ( t ): ( f(t x + f(t)) = f(x) f(t) + t )