Can this result in a expression of the form x^4?

[Klaramath]

Can this statement [math]\dfrac{(2a-1)^2-1}{2}=x^4[/math] ever be true? Be aware that a and x are both integers

 

[Deleted member 4993]

Can this statement [math]\dfrac{(2a-1)^2-1}{2}=x^4[/math] ever be true? Be aware that a and x are both integers

If I were to solve this problem, I would simplify the Left-hand-side of the given equation. Please share your work/thoughts and tell us exactly where you are stuck.

 

[BigBeachBanana]

I can see there are 2 "trivial" solutions, but I can't prove that those are the only ones yet...

 

[Harry_the_cat]

Can the statement ever be true? Is that the question? Then the answer is yes.
Just one of BBB's "trivial" solutions will suffice to answer the question as written.

Or are you required to find all such a and x?