Solve the diophanic equation $y^2 = x^4 -4x^3 + 6x^2 -2x +5$.
Methods I know:
1) look modulo p for some prime p, when using this method I almost always conclude there are no solutions, so i don't think it is handy to use this in this particular case.
2) Combinations of factorization and estimation: factorize your specific function and Search for an upper bound.
I used 2), and i get in a little bit of trouble.
I tried factorize the right hand side, but did not come any further then:
$y^2 - 10 = (x-5)(x^3 + x^2 - x - 3)$.
I don't seem to get an upper bound here..... :(.
Any hints on going to the right direction or on using a new method trying to solve this probelem?