The Fibonacci sequence is defined by the recurrence relation:
, where
and
.
Hence the first 12 terms will be:
The 12th term,
, is the first term to contain three digits.
What is the first term in the Fibonacci sequence to contain 1000 digits?
The sum of the squares of the first ten natural numbers is,
The square of the sum of the first ten natural numbers is,
Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 — 385 = 3640.
Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
So, apparently my brother has joined me on my Project Euler solving quest. You can see his Delphi solution on his blog. My C# solution, you can find below 
