p= 2: (1) Y^p=X+s^pX^p True, Y-sX=u True;  (2) (y-sx)^p-x = y^p-x-s^px^p True;  (3) dF/dx=-1 True
p= 3: (1) Y^p=X+s^pX^p True, Y-sX=u True;  (2) (y-sx)^p-x = y^p-x-s^px^p True;  (3) dF/dx=-1 True
p= 5: (1) Y^p=X+s^pX^p True, Y-sX=u True;  (2) (y-sx)^p-x = y^p-x-s^px^p True;  (3) dF/dx=-1 True
p= 7: (1) Y^p=X+s^pX^p True, Y-sX=u True;  (2) (y-sx)^p-x = y^p-x-s^px^p True;  (3) dF/dx=-1 True
p=11: (1) Y^p=X+s^pX^p True, Y-sX=u True;  (2) (y-sx)^p-x = y^p-x-s^px^p True;  (3) dF/dx=-1 True
p=13: (1) Y^p=X+s^pX^p True, Y-sX=u True;  (2) (y-sx)^p-x = y^p-x-s^px^p True;  (3) dF/dx=-1 True
all identities hold: True
sanity search p=2: tested 504 polynomials f, found 0 with f + t f^p a p-th power
sanity search p=3: tested 19656 polynomials f, found 0 with f + t f^p a p-th power
