# Canonical Decomp 2

• June 18th 2010, 10:10 PM
dwsmith
Canonical Decomp 2
Is there an easy way to approach this number or just start dividing away?

10,510,100,501
• June 19th 2010, 07:47 AM
Opalg
Quote:

Originally Posted by dwsmith
Is there an easy way to approach this number or just start dividing away?

10,510,100,501

Hint: $(x^2+1)^5 = x^{10} + 5x^8 + 10x^6 + 10x^4 + 5x^2 + 1$.
• June 19th 2010, 10:34 AM
dwsmith
I am not sure how that is supposed to help, but if I could see the connection, how would I know to come up with $(x^2+1)^5$?
• June 19th 2010, 11:56 AM
Opalg
Quote:

Originally Posted by dwsmith
I am not sure how that is supposed to help, but if I could see the connection, how would I know to come up with $(x^2+1)^5$?

Second (blatant) hint: Try putting x = 10 in that binomial expansion.

I have to admit that I cheated in order to find that method. (Itwasntme) I plugged the number 10510100501 in here in order to find the factors. When I saw the answer I could see why it came out that way.