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# AS Level Maths question HELP watch

1. Prove that if a number leaves a remainder 2 when it is divided by 3 then its square leaves a remainder 1 when divided by 3
2. (Original post by Zain786H)
Prove that if a number leaves a remainder 2 when it is divided by 3 then its square leaves a remainder 1 when divided by 3
Of course if you do this exercise using modular arithmetic it is very simple. If not then if a number x leaves a remainder of 2 when divided by 3 then it is of the form x=3y+2 where y is an integer.
So x^2=(3y+2)^2=9y^2+12y+4 and you should be able to show that this leaves a remainder of 1 when dividing by 3.
3. (Original post by B_9710)
Of course if you do this exercise using modular arithmetic it is very simple. If not then if a number x leaves a remainder of 2 when divided by 3 then it is of the form x=3y+2 where y is an integer.
So x^2=(3y+2)^2=9y^2+12y+4 and you should be able to show that this leaves a remainder of 1 when dividing by 3.
Thank you for the response but could you explain to me how you get x = 3y + 2 as I thought it would be
x/3 +2 as the first part
4. (Original post by Zain786H)
Thank you for the response but could you explain to me how you get x = 3y + 2 as I thought it would be
x/3 +2 as the first part
Because you divided it to get the answer, therefore you have to multiply to find the original number.
5. (Original post by CCauston113)
Because you divided it to get the answer, therefore you have to multiply to find the original number.
I understand now, thank you

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