2 large prime numbers, so only rectangle with side 2 will pass

2*3 is 6 so you would multiply that twice. Number with most divisors below 10^9 has more than 1000 divisors

a*Vix-Viy = a*Vjx — Vjy plus the condition Vi!=Vj is equivalent to the system of equations that describe a collision. Equivalence gives us both necessity and sufficiency.

Divide and Qounquer