MathDB

11.2

Part of IV Soros Olympiad 1997 - 98 (Russia)

Problems(3)

x^2 -\pi x+a < 0, 1998 integer solutions (IV Soros Olympiad 1997-98 R2 11.2)

Source:

6/1/2024
Find all values of the parameter aa for which there are exactly 19981998 integers xx satisfying the inequality x2−πx+a<0.x^2 -\pi x +a < 0.
number theoryalgebrainequalities
(y^3-arcsinx)(x^3+arcsin y)&gt;=0 (IV Soros Olympiad 1997-98 Correspondence 11.2)

Source:

6/1/2024
Find the area of a figure consisting of points whose coordinates satisfy the inequality (y3−arcsinx)(x3+arcsiny)≥0.(y^3 - arcsin x)(x^3 + arcsin y) \ge 0.
inequalitiesalgebratrigonometryanalytic geometry
3-digit with max no of different divisors (IV Soros Olympiad 1997-98 R3 11.2)

Source:

6/2/2024
Find the three-digit number that has the greatest number of different divisors.
number theoryDivisors