If :$A=1!2!\cdots 1002!$, and $B=1004 ! 1005!\cdots2006!$, how to prove that:
a) $2AB$ is a perfect square
b) $A+B$ is not a perfect square
If :$A=1!2!\cdots 1002!$, and $B=1004 ! 1005!\cdots2006!$, how to prove that:
a) $2AB$ is a perfect square
b) $A+B$ is not a perfect square