Question #231915

What is the largest integer n which makes n3 + 100 is divisible by n + 10


1
Expert's answer
2021-09-02T00:37:22-0400
n3+100=n3+1000900n^3+100=n^3+1000-900

=(n+10)(n2n+100)900=(n+10)(n^2-n+100)-900

The term (n+10)(n2n+100)(n+10)(n^2-n+100) is divisible by n+10.n+10.

The Divisors of 900 are as follows:

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, and 900.

We take n+10=900.n+10=900. Then n=890.n=890.

The largest nn which makes n3+100n^3+100 is divisible by n+10n+10 is therefore 890.890.



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