Before trying the problem "note your opinion as to whether the observed pattern is known to continue, known not to continue, or not known at all."

Does each of the two Diophantine equations have just the exact same five positive solutions of x = {1,2,3,6,91}?

2x²(x²-1) = 3(y²-1)
x(x-1)/2 = 2^z-1