The idea is to complete squares.
Find a likely candidate, e.g. from here: A026374: 1,6,11,6,1.
Then (x^4+6x^3+11x^2+6x+1) - y = x^4+x^3+x^2+x+1
and y = (5x^3+10x^2+5x)
(x^4+6x^3+11x^2+6x+1) - (5x^3+10x^2+5x)=x^4+x^3+x^2+x+1
But (x^4+6x^3+11x^2+6x+1) = (x^2+3x+1)^2
And (5x^3+10x^2+5x) = 5x(x+1)^2
Now since x=5^25, 5x=x^26, in which case (5^13)^2(x+1)^2, completes a difference of squares that can be factored:
[(x^2+3x+1)-(5^13)(x+1)]*[(x^2+3x+1)+(5^13)(x+1)]
Very pretty.
Edited on December 21, 2012, 7:35 am
|
|
Posted by broll
on 2012-12-21 07:04:27 |
Try this
