Algebra Question # 12: Divisibility is Love <3

Number Theory Level 3

How many integers x such that ­ x 5 + x 4 + x 3 + x 2 + x + 24 x^5+x^4+x^3+x^2+ x+ 24 is divisible by x and x>-12

Algebra Question

24 infinitely many solution 14 12

Paul Ryan Longhas by Paul Ryan Longhas , 24, Philippines

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2 solutions

x 5 + x 4 + x 3 + x 2 + x + 24 x^5+x^4+x^3+x^2+x+24 is divisible by x => 24 is also divisible by x. So, x = { 1,2,3,4,6,8,12,24, -1, -2, -3, -4,-6, -8} we cannot include x ={ -12, -24} since x>-12. So, the answer is 14 ( number of integers x)

3 Helpful 0 Interesting 0 Brilliant 0 Confused

What do you mean by your very first statement?

Raven Herd - 6 years, 3 months ago
Aayush Patni
Feb 24, 2015

Too simple. This should be level 2

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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