The motivation for starting Project Euler, and its continuation, is to provide a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context.
The intended audience include students for whom the basic curriculum is not feeding their hunger to learn, adults whose background was not primarily mathematics but had an interest in things mathematical, and professionals who want to keep their problem solving and mathematics on the cutting edge.
The first and second number in the sequence equals one, and each next element is the sum of the two previous elements in the sequence.
For more details see Fibonacci number (on Wikipedia).
Let's write a program which computes the nth Fibonacci number and then for two neighbouring such numbers, find a way to compute their greatest common divisor, . The greatest common divisor of two Fibonacci numbers. Write a generic function to compute Fibonacci numbers for a given variable. Finally, put the first into the second and I’ll get the greatest common divisor of two Fibonacci numbers.
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I present the function based on the formula, and it is pretty simple.
You can use a debugger to move step by step and check how this function works - this is useful when something goes wrong. I think the Fibonacci function is not efficient enough.
I can compute an array and then choose neighboring entries.
While studying mathematics, I read a book named “How to solve it”, about simplifying complex problems.
It was about heuristics - very direct (though not necessarily the most efficient) ways of getting solutions.