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Rational Rigor II (Posted on 2013-03-16)

Determine all possible rational numbers r such that 3r³ +10r² - 3r is an integer.

No Solution Yet Submitted by K Sengupta

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allof tem - spoiler

| Comment 1 of 3

Clearly, all integer values of r satisfy the polinom being integer.

If we are lookin for fraction , it nust be n/3, n being an integer.

Then the polynom becomes 1/9 *n*(n^2+10*n-27).

n^2+10*n =n*(n+10), divisible by 9 iff n=0 mod 9 or 8 mod 9.

Therefore r= any integer

or r= 8/3,17/3.26/3 ...

and -1/3, -10/3, -19/3... etc.

Edited on March 17, 2013, 6:24 am

Posted by Ady TZIDON on 2013-03-17 05:06:00

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