MathDB

7

Part of 2008 AIME Problems

Problems(2)

Sets Without Squares

Source: AIME 2008I Problem 7

3/23/2008
Let Si S_i be the set of all integers n n such that 100i\leq n < 100(i \plus{} 1). For example, S4 S_4 is the set 400,401,402,…,499 {400,401,402,\ldots,499}. How many of the sets S0,S1,S2,…,S999 S_0, S_1, S_2, \ldots, S_{999} do not contain a perfect square?
AMCinequalitiesnumber theoryIntermediate Number Theory
Cubic Roots

Source: AIME 2008II Problem 7

4/3/2008
Let r r, s s, and t t be the three roots of the equation 8x^3\plus{}1001x\plus{}2008\equal{}0.Find (r\plus{}s)^3\plus{}(s\plus{}t)^3\plus{}(t\plus{}r)^3.
VietaAMCAIMEalgebrapolynomialAIME I