Table of Contents
1 Problem
Consider all integer combinations of \(a^b\) for 2 \(\leq\) a \(\leq\) 5 and 2 \(\leq\) b \(\leq\) 5:
\(2^2\) =4, \(2^3\) =8, \(2^4\) =16, \(2^5\) =32 \(3^2\) =9, \(3^3\) =27, \(3^4\) =81, \(3^5\) =243 \(4^2\) =16, \(4^3\) =64, \(4^4\) =256, \(4^5\) =1024 \(5^2\) =25, \(5^3\) =125, \(5^4\) =625, \(5^5\) =3125
If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
How many distinct terms are in the sequence generated by \(a^b\) for 2 \(\leq\) a \(\leq\) 100 and 2 \(\leq\) b \(\leq\) 100?
2 Solution
Set集合
3 Answer
9183
Source:C++