Canonical Decomp 2

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June 18th 2010, 09:10 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, 06:47 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, 09:34 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, 10:56 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.

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