.
factorise x^4 + 4^2023.
~~~~~~~~~~~~~~~~~~~~~
Let' start writing
    =
 =  =
 =  =
 =  =
 =  .
It has the form
.
It has the form  ,  where  a =
,  where  a =  .
Now we will factor  the binomial
.
Now we will factor  the binomial   by some tricky way
  by some tricky way
       =
 =  =
 =  -
 -  = 
    
    = factorize as the difference of squares =
 = 
    
    = factorize as the difference of squares =  =
 =  .
Now substitute  a =
.
Now substitute  a =  into this formula.  Notice that
  into this formula.  Notice that   =
 =  =
 =  =
 =  =
 =  .  
You will get
.  
You will get
     =
 =  ,
or, which is the same,
,
or, which is the same,
     =
 =  .
It is the desired factorization.
.
It is the desired factorization.
Solved.
In whole,  it looks like a miracle.
I would say more :   not only it looks like a miracle,  it   a miracle.
  a miracle.