I have been playing around with factorising x^n-1 for positive integers n.

For example, x^2-1 = (x-1)(x+1)

X^3-1 = (x-1) ( x^2+x+1).

I have been using Wolfram to see what happens as n gets large: x^105-1

(x - 1) (x^2 + x + 1) (x^4 + x^3 + x^2 + x + 1) (x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) (x^8 - x^7 + x^5 - x^4 + x^3 - x + 1) (x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1) (x^24 - x^23 + x^19 - x^18 + x^17 - x^16 + x^14 - x^13 + x^12 - x^11 + x^10 - x^8 + x^7 - x^6 + x^5 - x + 1) (x^48 + x^47 + x^46 - x^43 - x^42 -2x^41 - x^40 - x^39 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 - x^28 - x^26 - x^24 - x^22 - x^20 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 - x^9 - x^8 -2x^7 - x^6 - x^5 + x^2 + x + 1)

I noticed that this is the first time to coeff of the terms are not -1, 0 or 1 . The above in bold has a '2'

I can't see why 105 would do this but not others?

Any ideas?