All numbers are not one of 3n, 3n+1 or 3n+2 (unless n can be 1/3, 2/3, etc.). In that case surely you could say that for any number of ns. For example x is one of 100n, 100n+1, 100n+2, 100n+3, ... and prove that it is a multiple of 1600?
This doesn't make sense to me, can you explain more?
All numbers are not one of 3n, 3n+1 or 3n+2 (unless n can be 1/3, 2/3, etc.). In that case surely you could say that for any number of ns. For example x is one of 100n, 100n+1, 100n+2, 100n+3, ... and prove that it is a multiple of 1600?
This doesn't make sense to me, can you explain more?
All integers are of the form 3n, 3n+1, 3n+2
I have assumed that x is an integer - otherwise your question does not actually make sense
Not sure what you mean with the 1600 but as that would not work
I have assumed that x is an integer - otherwise your question does not actually make sense
Not sure what you mean with the 1600 but as that would not work
Sorry, I should have specified. x is an interger. Yes, I now understand what you mean by all intergers are of form 3n, 3n+1, 3n+2. However are all intergers not also of the form 4n, 4n+1,4n+2,4n+3 and 5n,5n+1 etc...
I don't understand how this effects the question though. Could you please explain in a bit more detail how what you said effects the proof?
I still don't understand though. could you please explain in a bit more detail how what you said effects the proof?
thanks
If x is an integer and you divide it by 3, there are 3 possible results:
remainder 0 i.e. x is divisible by 3 i.e. x = 3n for some integer n remainder 1 i.e. x = 3n + 1 for some integer n remainder 2 i.e. x = 3n + 2 for some integer n
Have you tried putting the possibilities into the original expression
All should become clear
Yes, I have tried up to x=10 and all work. But I still don't understand how you can prove this. Please can someone talk me through the steps they would take?
Edit: Are you telling me to sub 3n, 3n+1 and 3n+2 into the equation and see if they come out with multiples of 48?
Yes, I have tried up to x=10 and all work. But I still don't understand how you can prove this. Please can someone talk me through the steps they would take?
SO you have not put the possibilities in
The steps I would take
Realise that 3 x 16 is 48 Realise that all integers are of one of these forms 3n 3n+1 3n+2 Put these options into the original statement Look for a factor of 3 in a bracket Show the 48 is a factor
Realise that 3 x 16 is 48 Realise that all integers are of one of these forms 3n 3n+1 3n+2 Put these options into the original statement Look for a factor of 3 in a bracket Show the 48 is a factor
Ok thank you! I now understand and all forms work.
I would say that is implied by the fact that x is greater than or equal to 1
Ok thanks, sorry for the silly comments earlier then, I was overlooking the fact that n could also = 0 (when x = 3n+1 and when x = 3n+2, but not when x = 3n)
Ok thanks, sorry for the silly comments earlier then, I was overlooking the fact that n could also = 0 (when x = 3n+1 and when x = 3n+2, but not when x = 3n)