Cramér's theorem states that if 
and 
are independent
variates and 
is a normal distribution, then both 
and 
must have normal distributions.
This was proved by Cramér in 1936.
Cramér's Theorem
See also
Normal DistributionExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Cramér's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CramersTheorem.html