Fermat's Last Theorem: n = 4

The easiest proof for Fermat's Last Theorem is the case n = 4 (a^4 + b^4 = c^2)

See solution at

http://fermatslasttheorem.blogspot.com/2005/05/fermats-last-theorem-n-4.html

How about the equation a^4 + b^4 + 1 = c^2

Could we still prove that there is no solution in the positive integers for this equation?

Could you provide a counter-example?

Fermat's Last Theorem

http://en.wikipedia.org/wiki/Fermat's_Last_Theorem

http://mathworld.wolfram.com/FermatsLastTheorem.html

Pierre de Fermat

http://en.wikipedia.org/wiki/Pierre_de_Fermat