The cyclotomic polynomials (http://en.wikipedia.org/wiki/Cyclotomic_polynomial) can be defined recursively by:

C1[X] = X-1
Cn[X] = (X^n-1) / Product { 1 <= d < n & d divides n } Cd[X]
It can be proved that all Cn[X] have integer coefficients.

Here are the first values:
  C1 = x^1-1
  C2 = x^1+1
  C3 = x^2+x^1+1
  C4 = x^2+1
  C5 = x^4+x^3+x^2+x^1+1
  C6 = x^2-1.x^1+1
  C7 = x^6+x^5+x^4+x^3+x^2+x^1+1
  C8 = x^4+1
  C9 = x^6+x^3+1
 C10 = x^4-1.x^3+x^2-1.x^1+1
 C11 = x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x^1+1
 C12 = x^4-1.x^2+1
 C13 = x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x^1+1
 C14 = x^6-1.x^5+x^4-1.x^3+x^2-1.x^1+1
 C15 = x^8-1.x^7+x^5-1.x^4+x^3-1.x^1+1

We define:
H[n]: the height of the n-th cyclotomic polynomial: its largest coefficient in absolute value.
F[h]: the index of the first cyclotomic polynomial whose height is h.
I[n]: the degre of the first monomial which reaches H[n] (in absolute value).

You are given:
C105 = x^48+x^47+x^46-1.x^43-1.x^42-2.x^41 ... x^12-1.x^9-1.x^8-2.x^7-1.x^6-1.x^5+x^2+x^1+1
H[105]=2
F[2]=105
I[105]=7

What is F[3],I[F[3]]?

Answer format: values comma separated

Example: 105,7
[My timing : < 100 ms]

P.S:
You don\\\'t have to have a C.A.S (http://en.wikipedia.org/wiki/Computer_algebra_system) to tackle this problem (even if it helps I guess...).
I don\\\'t.