OK thank you for your reply and your encouragement.

If you calculate all numbers up to ~1.5M, then, unfortunately, your approach is not correct. You'd have to search for some algorithm to calculate Nth Fibonacci number without calculating all numbers below N. Even with memoization, "regular" approach will be probably too slow.

There are algorithms which calculate Nth Fibonacci number with fewer intermediate steps. Try researching a bit more, their descriptions are not very difficult to find.

I can get my code to run fine up to about n=1,000,000 but after that it times out. It does run to completion on my computer in about 20 seconds. I'm using a simple for..loop. Can anyone give me some guidance on where to look to how to improve the performance of my code for values of n between 1 million and 2 million?

I'm actually very satisifed that I have cracked the test and pretty much ticked all the boxes apart from this last one.

PS I'm using Java!