Largest Positive IntegerDate: 11/04/2002 at 15:14:07 From: Victoria Szabuniewicz Subject: Largest positive integers What is the largest positive integer n for which n^3 + 100 is divisible by n+10? I have tried to graph both equations, divide the two equations and then graph; then I tried to factor the equations. I have no idea what else to do and have come up with nothing but frustration. Thanks! Date: 11/06/2002 at 10:47:12 From: Doctor Jubal Subject: Re: Largest positive integers Hi Victoria, Thanks for writing Dr. Math. You're looking for numbers n such that n^3 + 100 ----------- n + 10 is an integer. If we perform long division on the polynomials, we find n^2 - 10n + 100 +----------------------- n + 10 | n^3 + 0n^2 + 0n + 100 n^3 + 10n^2 ----------- - 10n^2 - 10n^2 - 100n -------------- 100n + 100 100n + 1000 ----------- - 900 So n^3 + 100 900 --------- = n^2 - 10n + 100 - ------- n + 10 n + 10 And for the original fraction to be an integer, 900 must be divisible by n+10. What is the largest value of n such that n+10 divides 900? Does this help? Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Jubal, The Math Forum http://mathforum.org/dr.math/ Date: 11/06/2002 at 17:07:09 From: Victoria Szabuniewicz Subject: Thank you (Largest positive integers) Thank you so much for your help. It helped me immensely and I greatly appreciate it! |
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