Anyway i have some problems which i wonder if you guys here on D.I.C. can help me with by giving me tips for how to solve and how to think.

1. Knowing if a number is a prime.

- A prime number is a number that can only be divided by itself or 1. But how can i without testing all numbers from 2...n know in a quick way if a number is prime or not? How do you guys do?

Example task: Which of the following numbers are prime numbers: 171, 203, 211, 221?

2. Prime factorisation of big numbers.

Example task: Do a prime factorisation of a) 24^4 and 250^3

This one i do not really have a good idea on how to tackle. Do i have to get the number that for example 24^4 represents or can i factorize it just from its exponential form?

3. Proofs

- I have had this tas which i have tried to solve for over 2 hours and I'm completely stuck.

Task: Proove that 6 | n(n^2-1) for any integer n

I have came so far that i can put n(n^2-1) = 6 * x according to the division laws a|b a = b * c

Then i can change the form of n(n^2-1) to n * (n+1)(n-1) or n^3 - n but I'm not sure which way to go or how to solve this one.

If i change it to n^3 - n = 6 * x i can move the -n to the other side and get n^3 = 6 * x+n but it doesn't get me closer to proving its divisable with 6.

I think what i have to do is make a variable for example b like i could do with for example a-1 = 4b then a = 4b+1 but i cannot wrap my head around this problem and its driving me nuts. Any help or pushes in the right direction is appreciated!

Sorry for bad formatting this was written from my phone.

Thanks

This post has been edited by **Brokenprogrammer**: 03 September 2016 - 02:55 AM