Fermat number product identity (${\prod }_{j=0}^{n-1}{F}_j=F_n-2$)

For each positive integer $n$, the product of the preceding Fermat numbers is two less than the next:For example, $3\cdot 5\cdot 17=255=257-2$. The identity telescopes by repeated difference of squares: $(2^{2^j}-1)(2^{2^j}+1)=2^{2^{j+1}}-1$. Its usefulness is that a huge integer product exposes a tiny difference, two, from the next term.