ROMANIAN MATHEMATICAL MAGAZINE-R.M.M.-summer 2016
PROBLEMS FOR JUNIORS
JP.001.Let be non-negative real numbers such that:
.Prove that:
Proposed by Hung Nguyen Viet-Hanoi-Vietnam
JP.002.Let be real numbers greater than and satisfying:
Prove that:
Proposed by Hung Nguyen Viet-Hanoi-Vietnam
JP.003.Let be such that:
Prove that:
Proposed by Leonard Giugiuc-Romania
JP.004.Let beși . Prove that:
Proposed by D. M. Bătinețu – Giurgiu; NeculaiStanciu-Romania
JP.005.Prove that if then:
Proposed by D. M. Bătinețu – Giurgiu; NeculaiStanciu-Romania
JP.006.Prove that if: then:
Proposed by Daniel Sitaru-Romania
JP.007.Prove that if: then:
Proposed by Daniel Sitaru-Romania
JP.008.If are the lenght’s sides in any triangle the following relationship doesn’t holds:
Proposed by Redwane El Mellass-Morocco
JP.009.Prove that if then:
Proposed by Daniel Sitaru-Romania
JP.010.Prove that:
Proposed by Kevin Soto Palacios-Peru
JP.011.
JP.012.Prove that if: then:
Proposed by Daniel Sitaru-Romania
JP.013.If solve for real numbers the equations:
and
Proposed by Dana Heuberger-Romania
JP.014.If then:
Proposed by Regragui El Khammal-Morocco
JP.015.Prove that if then:
Proposed by Daniel Sitaru-Romania
PROBLEMS FOR SENIORS
SP.001.Let be non-negative real numbers such that:
. Prove that:
Proposed by Hung Nguyen Viet-Hanoi-Vietnam
SP.002.Prove that in any acute-angledthe following relationsip holds:
Proposed by Daniel Sitaru-Romania
SP.003.
SP.004.If then:
Proposed by Daniel Sitaru-Romania
SP.005.Let be such that: Prove that:
. When equality holds?
Proposed by Leonard Giugiuc-Romania
SP.006.Let be such
that: .Prove that:
Proposed by Leonard Giugiuc-Romania
SP.007.If are the length sides in any trianglethen:
Proposed by D.M. Bătinețu – Giurgiu; NeculaiStanciu-Romania
SP.008.Prove that if: then:
Proposed by MihalyBencze-Romania
SP.009.Let be
continuous,bijectifs and strictly increasing functions.Prove that:
Proposed by Daniel Sitaru-Romania
SP.010. Solve in complex numbers for :
Proposed by Leonard Giugiuc-Romania
SP.011.
SP.012.Find:
Proposed by Daniel Sitaru-Romania
SP.013.Find:
Proposed by AyadReda-Algerie
SP.014.Prove that if ; then:
Proposed by Daniel Sitaru-Romania
SP.015.Let be ind:
Proposed by DanNedeianu-Romania
UNDERGRADUATE PROBLEMS
UP.001.Prove that if then:
Proposed by Daniel Sitaru-Romania
UP.002.Prove that if
then:
Proposed by Daniel Sitaru-Romania
UP.003.Prove that exists:such that:
Proposed by Leonard Giugiuc-Romania
UP.004.Let bea continuos, convexe function on
. Prove that if then:
Proposed by Daniel Sitaru-Romania
UP.005.If then: .
Proposed by Leonard Giugiuc-Romania
UP.006.If then:
Proposed by Leonard Giugiuc-Romania
UP.007. Let be
. Find:
Proposed by D.M. Bătinețu – Giurgiu; NeculaiStanciu-Romania
UP.008.Find:
Proposed by MihalyBencze-Romania
UP.009.Prove that ifthen:
Proposed by MihalyBencze-Romania
UP.010.Find:
Proposed by Daniel Sitaru-Romania
UP.011.
UP.012.
UP.013.Let be a ring with . If are such that prove that and are inversables.
Proposed by NicolaePapacu-Romania
UP.014. Prove that:
Proposed by Daniel Sitaru-Romania
UP.015.Let be the ring . If exists such that :
then the ring it’s a commutative one.
Proposed by Dana Heuberger-Romania
R.M.M.-ROMANIAN MATHEMATICAL MAGAZINE-SUMMER 2016