Henson jfsihenson at gmail.com
Thu Jan 5 18:16:57 UTC 2017

```Hi,

Firstly I desire one year brilliant for all on group.

I have one simple problem but not solved for me for some mistake mine.

I have one Rational number (3 + sqrt 5) and I need get the last three
digits from

integral part of that number.

The question is the number is arbitrary and that number always is power
of n and n is between 2(Two) and 2000000000(Two billions).

I have attempted that on ghci for various values and get same result
with different powers:

let x = (truncate ((3 + sqrt 5) ^ 2000000)) `mod` 1000 and result is 216.

let y = (truncate ((3 + sqrt 5) ^ 20000000)) `mod` 1000 and result is 216.

let w = (truncate ((3 + sqrt 5) ^ 200000000)) `mod` 1000 and result is 216.

let z = (truncate ((3 + sqrt 5) ^ 2000000000)) `mod` 1000 and result is 216.

The result is same for all:

216, and is incorrect because any that expressions have one exclusive value.

What I do for complete that task correctly and what I'm mistaken here?!

Thank you,

Josenildo Silva

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