MathDB

13

Part of 2006 AIME Problems

Problems(2)

Power of 2 Function

Source: 2006 AIME I Problem 13

3/9/2006
For each even positive integer xx, let g(x)g(x) denote the greatest power of 22 that divides xx. For example, g(20)=4g(20)=4 and g(16)=16g(16)=16. For each positive integer nn, let Sn=∑k=12n−1g(2k).S_n=\sum_{k=1}^{2^{n-1}}g(2k). Find the greatest integer nn less than 10001000 such that SnS_n is a perfect square.
functionAMC
Numtheory

Source: 2006 AIME II 13

3/28/2006
How many integers N N less than 1000 can be written as the sum of j j consecutive positive odd integers from exactly 5 values of j≥1 j\ge 1?
floor functionAMC