1. ## Number theory equations

Solve the following equations positive integers:

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

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

(iii)a!=b^2

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??

2. ## Re: Number theory equations

Originally Posted by Sonifa
(i) a!+b!+c!=d!
Hi Sonifa!

Let's pick $a \le b \le c$.

Then we have $d! = a!+b!+c! \le 3c!$.
Therefore $d \le 3$.
Now enumerate all possibilities taking this bound into account...