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Hello Bunuel - thank you so much for this fantastic post!

with regards to checking for primality:

Quote:

Verifying the primality (checking whether the number is a prime) of a given number can be done by trial division, that is to say dividing by all integer numbers smaller than , thereby checking whether is a multiple of . Example: Verifying the primality of : is little less than , from integers from to , is divisible by , hence is not prime.

Would it be accurate to say that a number is prime ONLY if it gives a remainder of 1 or 5 when divided by 6? i.e, for eg. 10973/6 gives a remainder of 5, so it has to be prime...

i found the reasoning behind this in one of the OG solutions: prime numbers always take the form: 6n+1 or 6n+5 ....

the only possible remainders when any number is divided by 6 are [0,1,2,3,4,5] ... A prime number always gives a remainder of 1 or 5, because: a) if the remainder is 2 or 4, then the number must be even b) if the remainder is 3, then it is divisible by 3 ...

hence, if a number divided by 6 yields 1 or 5 as its remainder, then it must be prime ...?

But: Not all number which yield a remainder of 1 or 5 upon division by 6 are prime, so vise-versa of above property is not correct. For example 25 yields a remainder of 1 upon division be 6 and it's not a prime number.

Hope it's clear.

Understood Sir! .. i'll just use it one way; i.e, if i'm told that n is a prime number>3, then i can express it as 6n+1 or 6n+5

I think I just got a bit too excited about it that I forgot to thoroughly test it thru...

For determining last digit of a power for numbers 0, 1, 5, and 6, I am not clear on how to determine the last digit.

Your post says: • Integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base.

What is the last digit of 345^27 ---is the last digit 5? What is the last digit of 216^32----is the last digit 6? What is the last digit of 111^56---is the last digit 1?

I am having a small confusion between two concepts for which one of my practice Q went wrong. During my elementary school I have studied BODMAS B - Brackets O - Of D- Division M-Mulitplication A- Addition S- Substraction

I tried with this approach and it went wrong, while i was going through this again i happened to see a difference between PEMDAS & BODMAS (Multiplication order is different) .

Can somebody help me to understand which one i should follow.

I am having a small confusion between two concepts for which one of my practice Q went wrong. During my elementary school I have studied BODMAS B - Brackets O - Of D- Division M-Mulitplication A- Addition S- Substraction

I tried with this approach and it went wrong, while i was going through this again i happened to see a difference between PEMDAS & BODMAS (Multiplication order is different) .

Can somebody help me to understand which one i should follow.

Thanks Humble GMAT ASPIRANT

The rule mentioned in the initial post is correct.

Anyway: what difference are you talking about? Can you give an example?
_________________

Any nonzero natural number n can be factored into primes, written as a product of primes or powers of primes. Moreover, this factorization is unique except for a possible reordering of the factors.

Pls give me the example of bold face text because i am not sure what does it exactly means.

Thanks
_________________

The proof of understanding is the ability to explain it.

gmatclubot

Re: Math: Number Theory
[#permalink]
27 Feb 2011, 09:04

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