A Pythagorean triplet is a set of three natural numbers, $a < b < c$, for which, \[a^2 + b^2 = c^2\]
For example, $3^2 + 4^2 = 9 + 16 = 25 = 5^2$.
There exists only one Pythagorean triplet for which $a + b + c = 1000$. Find the product $abc$.
The four adjacent digits in the 1000-digit number that have the graetest product are \[9\times 9\times 8\times 9 = 5832\]
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By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
What is the 10,001st prime number?
The sum of the squares of the first ten natural numbers is, \[1^2 + 2^2 + \cdots + 10^2 = 385\]
The square of the sum of the first ten natural numbers is, \[(1 + 2 + \cdots + 10)^2 = 55^2 = 3025\]
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 by 1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible by all 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 x 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 20 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89
By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terrms.
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.
