Used to prove that there is no general method for solving Diophantine equations, methods for computing them include Cassini's identity, Binet's formula, and determining how many ways there are to tile a 2-by-n strip with 1-by-2 rectangles.  One may also expand their generating function: f-of-x equals x divided by 1 minus x 
Used to prove that there is no general method for solving Diophantine equations, methods for computing them include Cassini's identity, Binet's formula, and determining how many ways there are to tile a 2-by-n strip with 1-by-2 rectangles.  One may also expand their generating function: f-of-x equals x divided by 1 minus x minus x-squared, or sum the shallow diagonals of Pascal's triangle to compute, FTP, what sequence of numbers, whose first five members are 1, 1, 2, 3, 5?
Used to prove that there is no general method for solving Diophantine equations, methods for computing them include Cassini's identity, Binet's formula, and determining how many ways there are to tile a 2-by-n strip with 1-by-2 rectangles.  
Fibonacci numbers