MathDB

1

Part of 2002 Hungary-Israel Binational

Problems(2)

$x^3 + y^4\leq x^2 + y^3$

Source: 13-th Hungary-Israel Binational Mathematical Competition 2002

4/7/2007
Suppose that positive numbers xx and yy satisfy x3+y4≤x2+y3x^{3}+y^{4}\leq x^{2}+y^{3}. Prove that x3+y3≤2.x^{3}+y^{3}\leq 2.
inequalities proposedinequalitiesalgebra
Find the greatest exponent $k$

Source: 13-th Hungary-Israel Binational Mathematical Competition 2002

4/7/2007
Find the greatest exponent kk for which 2001k2001^{k} divides 200020012002+2002200120002000^{2001^{2002}}+2002^{2001^{2000}}.
number theory proposednumber theory