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        riddles >> medium >> 3xCubed + 10xSquared - 3x = Integer 
        
(Message started by: ThudanBlunder on Jan 20^th, 2009, 5:30pm)

Title: 3xCubed + 10xSquared - 3x = Integer
Post by ThudanBlunder on Jan 20^th, 2009, 5:30pm

For which (reduced) fractions x is 3x³ + 10x² - 3x an integer?

Title: Re: 3xCubed + 10xSquared - 3x = Integer
Post by balakrishnan on Jan 20^th, 2009, 11:15pm

[hideb]1)All integers n
2)The set of all fractions of the form x=(9n+ 8 )/3 where n is an integer and the corresponding 3*x^3+10*x^2-3*x is 81*n^3 + 306*n^2 + 343*n + 120[/hideb]