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