Posted by AuntieMel on January 16, 2007, at 9:17:37
In reply to Anyone good at number theory?, posted by linkadge on January 11, 2007, at 17:17:02
I found a property:GCD (a + b, b) = GCD (a, b)
So GCD (a^2 + b^2, a + b) = GCD (a^2, a + b).
The only possible cases for a and b are
1) a is odd, b is even
2) a is even, b is odd
3) a and b are both oddIn case 1, the GCD of (a^2, a + b) is 1
case 2, the GCD of (a^2, a + b) is 1 (a + b is odd)
case 3, the GCD of (a^2, a + b) is 2 (a + b is even)
poster:AuntieMel
thread:721428
URL: http://www.dr-bob.org/babble/social/20070112/msgs/722827.html