Largest Positive

n^3+100 mod n+10=0 change the left side into 100-10n^2 then 100+100n after that -900 and finally 900=> 900 mod n+10=0 => n+10 max for n^3+100 is divisible by n+10 is 900=>n=890. this is the idea. and i need advice or solution writting in english, thanks.

By division we find that n^3+100=(n+10)(n^2−10n+100)−900.

Therefore, if (n+10) divides (n^3+100), then it must also divide 900. Since we are looking for largest n, n is maximized whenever (n+10) is, and since the largest divisor of 900 is 900, we must have n+10=900⇒n=890 The largest n is therefore 890