Gay-Lussac law explanation
Gay-Lussac's Law, in its most basic form, says that, assuming constant volume (V) and amount/moles (n), the pressure (P) of a gas is directly proportional to the absolute temperature (T) of a gas.  We can write this mathematically in a couple different ways:

$$ P = kT$$
 (assuming constant V and n), where k is some constant.  More often, we use it in the form below, where we know the pressure and temperature under one set of conditions, and then change those conditions (again, keeping V and n constant):

$$ 
\frac{P_1}{T_1} = \frac{P_2}{T_2}
$$

As for the next statement, "all gases have the same amount of particles", as stated this makes no sense.  Perhaps what you meant to say was that, under identical conditions, equal volumes of an ideal gas contain equal number of moles (and therefore equal numbers of gas particles).  For example, it can easily be shown using the Ideal Gas Law that one mole of an ideal gas occupies 22.4 L at STP.