Euler Problem 29: Distinct Powers

Euler Problem 29 is another permutation problem that is quite easy to solve using brute force. The MathBlog site by Kristian Edlund has a nice solution using only pen and paper.

Raising number to a power can have interesting results. The video below explains why this pandigital formula approximates to billions of decimals:

Euler Problem 29 Definition

Consider all integer combinations of: for and .

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

How many distinct terms are in the sequence generated by for and ?

Brute Force Solution

This code simply calculates all powers from to and determines the number of unique values. Since we are only interested in their uniqueness and not the precise value, there is no need to use Multiple Precision Arithmetic.

# Initialisation
target <- 100
terms <- vector()
i <- 1
# Loop through values of a and b and store powers in vector
for (a in 2:target) {
   for (b in 2:target) {
     terms[i] <- a^b
     i <- i + 1
   }
}
# Determine the number of distinct powers
answer <- length(unique(terms))
print(answer)

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