find the maximum value of n for which - (n^3 + 100 )/(n + 10 ) is an integer
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For n = 1 0 , n + 1 0 n 3 + 1 0 0 = n 2 − 1 0 n + 1 0 0 − n + 1 0 9 0 0 .
Therefore, n + 1 0 n 3 + 1 0 0 is an integer if and only if n + 1 0 9 0 0 is an integer, and the largest such n is 8 9 0 .
Where is 900/n+10 coming from ??
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I used practically used the same method as Maggie, but I included the substitution step. i.e. u = n + 1 0 . I made this substitution because it is easier to deal with the fraction if the denominator is u rather than n+10.