The different types of numbers expressed algebraically: 

 

1. Even Numbers  =  2n  

2. Odd Numbers  =  2n + 1 

3. Square Numbers  =  n 

4. Multiples of integer x  =  xn 

5. Remainder of x when divided by y  =  yn + x 

6. Two Consecutive Integers  =  n , n+1 

7. Two Consecutive odd integers  =  2n+1 , 2n +3 

 

•  In order to tackle proof problems we need to use the algebra above 

• For Example: 

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​​   Prove that the sum of three consecutive positive integers is always a multiple of 3. 

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• First we create our integers: 

 

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• Here the question is asking about the sum, so we add our integers together 

 

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• We can see that the sum of our integers is equal to 3n, which is a multiple of 3  

• Therefore we have proved that the sum of 3 consecutive integers is a multiple of 3 

 

Question: 

 

 

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Solution: 

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