In this video I explain how to solve the following problems:
1. Prove that the square of any natural number is either a multiple of 3 or 1 more than a multiple of 3. [4 marks]
2. Given that a and b are natural numbers, prove that a^2+b^2 is only a multiple of 3 if both a and b are multiples of 3. [3 marks]
3. Richard states that a^2+b^2 is only a multiple of n if both a and b are multiples of n. State, giving a reason, whether this is always true, sometimes true, or never true. [2 marks]
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