TITLE: The number of group elements whose squares lie in a given subgroup
QUESTION [16 upvotes]: This number is divisible by the order of the subgroup  http://arxiv.org/abs/1205.2824.
The proof is short but non-trivial. Is this fact new or is it known for a long time?

REPLY [6 votes]: In 2017, we learned that this fact was proven by Shiro Iwasaki in 
1982.