Division problem

• October 5th 2009, 04:44 PM
streethot
Division problem
Find all $a,b\in\mathbb{Z}^+$ such that (ab²+b+7)|(a²b+a+b)
• October 5th 2009, 07:29 PM
tonio
Quote:

Originally Posted by streethot
Find all $a,b\in\mathbb{Z}^+$ such that (ab²+b+7)|(a²b+a+b)

Polynomial (in a) division:

a^2b + a + b | ab^2 + b + 7
____________|____________
a^b + a +7a/b| a/b
------------- |----------------------
b - 7a/b |

So it must be b - 7a/b = 0 ==> b^2 = 7a ==> a = 7k^2, b = 7k, k an integer.

Tonio