2

Part of 1996 Estonia National Olympiad

Problems(4)

(1996^{1995}+1)/(1996^{1996}+1) vs (1996^{1996}+1)/(1996^{1997}+1)

Source: 1996 Estonia National Olympiad Final Round grade 10 p2

Which number is greater,

\frac{1996^{1995}+1}{1996^{1996}+1}

\frac{1996^{1996}+1}{1996^{1997}+1}

reverse digits and have two times bigger number

Source: 1996 Estonia National Olympiad Final Round grade 9

Does there exist a positive integer such that its last digit is nonzero and that it becomes exactly two times bigger when the order of its digits is reversed?

number theoryDigits

angles trapezoid wanted, 3 equal sides and a circle related

Source: 1996 Estonia National Olympiad Final Round grade 11 p2

Three sides of a trapezoid are equal, and a circle with the longer base as a diameter halves the two non-parallel sides. Find the angles of the trapezoid.

geometrytrapezoidanglesequal segments

min of x^{1000}+x^{900}+x^{90}+x^6+ 1996/x for x>0

Source: 1996 Estonia National Olympiad Final Round grade 12 p2

For which positive

x

does the expression

x^{1000}+x^{900}+x^{90}+x^6+\frac{1996}{x}

attain the smallest value?

mininequalitiesalgebra