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Thursday, January 21, 2010

Maths Homework

How do you know if a number is divisible by:
2
3
4
5
9
10
11

2: If the number ends with a 0, 2, 4, 6 or 8, the number is divisible by 2.
3: If all the digits in the number add up to be a multiple of 3, the number is divisible by 3.
4: Every alternate multiple of 2 is divisible by 4.
5: If the number ends with 0 or 5, the number is divisible by 5.
9: Any number divisible by 3 can be divided by 9.
10: If a number ends with a 0, the number is divisible by 10.
11: If a two digit number has two similar digits (e.g. 22, 55), it divisible by 11.

A mathematician proposed that "Every even number greater than 2 can be expressed as a sum of two prime numbers." Do you agree? Why?

Yes, I agree.

Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:

Every even integer greater than 2 is a Goldbach number, a number that can be expressed as the sum of two primes.

The number of ways an even number can be represented as the sum of two primes[2]

Expressing a given even number as a sum of two primes is called a Goldbach partition of the number. For example,

4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 7 + 3 = 5 + 5
12 = 5 + 7
14 = 3 + 11 = 7 + 7
From http://en.wikipedia.org/wiki/Goldbach's_conjecture

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