Question 48
For the natural number $N = p_1^{a_1} p_2^{a_2} \dots p_n^{a_n}$, written in the canonical form ($p_i$ are distinct primes and $a_i$ are naturals, $1 \le i \le n$), we denote $T(N) = a_1 + a_2 + \dots + a_n$. For some distinct natural $a, b, c, d$ the number $ab + cd$ is divisible by $ac + bd$. Prove that $T(ab + cd) \ge 3$.