What is the maximum value of n k a 6 b 7 c 8 d 9 e 10

. What is
the maximum value of N ( k ) ?
(A) 6 (B) 7 (C) 8 (D) 9 (E) 10
2009 AMC 10 A, Problem #25 —
2009 AMC 12 A, Problem #18 —
“Note that I
k
= 2
k +2
· 5
k +2
+ 2
6
.”
Difficulty: Hard
NCTM Standard: Algebra Standard: understand meanings of operations and how they relate to
one another.
Mathworld.com Classification: Number Theory > Prime Numbers > Prime Factorization >
Prime Factorization