MathDB

4

Part of 2008 AIME Problems

Problems(2)

Equation over Integers

Source: AIME I 2008 Problem 4

3/23/2008
There exist unique positive integers x x and y y that satisfy the equation x^2 \plus{} 84x \plus{} 2008 \equal{} y^2. Find x \plus{} y.
trigonometryAMCAIMEquadraticsLaTeXspecial factorizationsDiophantine equation
Sum of Powers of 3

Source: AIME 2008II Problem 4

4/3/2008
There exist r r unique nonnegative integers n1>n2>⋯>nr n_1 > n_2 > \cdots > n_r and r r unique integers ak a_k (1≤k≤r 1\le k\le r) with each ak a_k either 1 1 or \minus{} 1 such that a_13^{n_1} \plus{} a_23^{n_2} \plus{} \cdots \plus{} a_r3^{n_r} \equal{} 2008. Find n_1 \plus{} n_2 \plus{} \cdots \plus{} n_r.
AMCAIME2008