The sum of the squares of the first ten natural numbers is,
$$1^2 + 2^2 + … + 10^2 = 385$$
The square of the sum of the first ten natural numbers is,
$$(1 + 2 + … + 10)^2 = 55^2 = 3025$$
Hence the difference between the sum of the squares of the first ten natural
numbers and the square of the sum is $3025 - 385 = 2640$.
Find the difference between the sum of the squares of the first one hundred
natural numbers and the square of the sum.
2520 is the smallest number that can be divided by each
of the numbers from 1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible
by all of the numbers from 1 to 20?
A palindromic number reads the same both ways. The largest palindrome
made from the product of two 2-digit numbers is $9009 = 91 \times 99$.
Find the largest palindrome made from the product of two 3-digit numbers.
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143 ?
Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
$$
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …
$$
Find the sum of all the even-valued terms in the sequence which do not exceed four million.
If we list all the natural numbers below 10 that are multiples of 3 or 5, we
get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.