AS Level Maths question HELP

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

Reply 1

B_9710

18

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.

Reply 2

Zain786H

OP

10

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

Reply 3

CCauston113

14

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.

Reply 4

Zain786H

OP

10

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

Reply 5

askingalevel19

4

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.