Question

Add all the numbers formed by squaring each of the three successive natural numbers and find the remainder when it is divided by 3.

Answer 1

I solved this using Python, but you can definitely do this mathematically

n^2 + (n+1)^2 + (n+2)^2 can be expanded into
3n^2 + 6n + 5

I hope you know of the mod function, which tells us the remainder
a mod b = c
This means a divided by b gives us a remainder of c

Lets take a look at each term:
3n^2 mod 3 = 0, since 3n^2 is definitely divisible by 3
6n mod 3 = 0, since 6n is definitely divisible by 3
5 mod 3 = 2, since 3 only goes into 5 one time, and then there is a remainder of 2

So lets write that out as 3n^2 mod 3 + 6n mod 3 + 5 mod 3 = 0 + 0 + 2 = 2

The remainder then, should always be equal to 2! Hope this makes sense, and if you have questions I'm happy to answer

Answer 2

Thank you though.

Answer 3

@silvernight269 @noodlesandriceyt