What are the solutions to these number theory equations?

[Funky1981]

Homework Statement

Solve the following equations positive integers:

(i) a!+b!+c!=d!

(ii) a!+b!=25*c!

(iii)a!=b^2

Homework Equations

For the first two one , i have no idea how to begin . But the third one I may use Bertrand's Postulate some where. Could anyone give me some ideas??

 

[mfb]

Do you have to find all solutions? The first one has a solution that is easy to find, and you can even prove that there are no other solutions. The second one has a solution with small numbers, too, but I'm not sure how to prove (with pen&paper) that there are no other solutions.

But the third one I may use Bertrand's Postulate some where.

That is a good idea.