MathDB

7

Part of 2017 AIME Problems

Problems(2)

Wot n' Binomial Notation

Source: 2017 AIME I #7

3/8/2017
For nonnegative integers aa and bb with a+b≤6a + b \leq 6, let T(a,b)=(6a)(6b)(6a+b)T(a, b) = \binom{6}{a} \binom{6}{b} \binom{6}{a + b}. Let SS denote the sum of all T(a,b)T(a, b), where aa and bb are nonnegative integers with a+b≤6a + b \leq 6. Find the remainder when SS is divided by 10001000.
2017 AIME IWot n
Fahrenheit 45one solution to logarithm equation

Source: 2017 AIME II #7

3/23/2017
Find the number of integer values of kk in the closed interval [−500,500][-500,500] for which the equation log⁡(kx)=2log⁡(x+2)\log(kx)=2\log(x+2) has exactly one real solution.
logarithmsAMCAIMEAIME IIgenius title