(In reply to
re(2): Errorless text Yes indeed by Ady TZIDON)
Wolfram Alpha gives (1 +/ i)/Sqrt[2] as the two values for a that satisfy the equation.
Then (a^777) + 1/(a^777), a=(1  i)/Sqrt[2] gives sqrt(2) as the answer; the same if a=(1 + i)/Sqrt[2] is given.

Posted by Charlie
on 20230422 08:39:01 