Let a= 3

and n large numbre like RSA-260

Code:

22112825529529666435281085255026230927612089502470015394413748319128822941402001986512729726569746599085900330031400051170742204560859276357953757185954298838958709229238491006703034124620545784566413664540684214361293017694020846391065875914794251435144458199

then

x private key

c= a

^{x} mod n

we can check if

x number is odd or even

We can use just

a,n,c to determine if

x number is even or odd.