I get really stuck with proof questions where you can't just find a number which shows it doesn't work. For example, how do you prove the square of an odd number is 1 more than a multiple of 4?

Hi
These questions can be tricky. You can't just put number in because you would have to show that it worked for every single number which is impossible, so we need to go back to our old friend algebra.
The key is to get the question set up right in the first place. So this question is about the square of an odd number s0 we have to "make" an odd number then square it.
To force a variable to be even we just times by 2, so instead of using "n" we use "2n". Ten to make it odd we add or subtract 1 - doesn't matter which. So I'm going to start with 2n + 1
The question then we have to square it:
(2n+1)^2 = 4n^2 + 4n + 1
The first two terms are both multiples of 4, so the whole thing is a multiple of 4 + 1.
Hope that helps!

cumbriamathstutor 26 minutes ago

Hi These questions can be tricky. You can't just put number in because you would have to show that it worked for every single number which is impossible, so we need to go back to our old friend algebra. The key is to get the question set up right in the first place. So this question is about the square of an odd number s0 we have to "make" an odd number then square it. To force a variable to be even we just times by 2, so instead of using "n" we use "2n". Ten to make it odd we add or subtract 1 - doesn't matter which. So I'm going to start with 2n + 1 The question then we have to square it: (2n+1)^2 = 4n^2 + 4n + 1 The first two terms are both multiples of 4, so the whole thing is a multiple of 4 + 1. Hope that helps!