i ended up using BigInt(dont know if its same as BigInteger) and it worked after some modifications, Thanks for the support.
this kata was over convoluted in my opinion, but I learned a lot, it was worth it!

Beware of overflow of your fractions: simplify them early, or maybe use biginteger.

Thanks for the quick response, yes I'm using JS, what should be done in this case?

surely your internal representation overflows at some point (I guess you're using JS)

I'm having a problem with the random tests with many digit fractions, I'm using exact arithmetics not floating point at all,
yet when the fraction gets with many digits the answer is wrong,
I guess it's a precision problem, did anyone face this problem?

its too vague, could you please add another example (below 7 eggs 20 tries)
i get 105 for 14 tries 2 eggs but for 7 eggs and 20 tries, i get a little more than 137979,
i tested some cases and it seems to work.
could it be that 137979 is not the actual maximum? maybe the boundaries(where an egg, each try is supposed to be dropped from) werent counted?