Rearrange the equation a bit: DEAL * (DEAL-1) = WXYZ0000
The right side is a multiple of 10000 = 2^4 * 5*4. Then DEAL and DEAL-1 are in some order a multiple of 2^4=16 and a multiple of 5^4=625.
The multiple of 625 will be odd, then the possible four digit options are 625*3=1875, 625*5=3125, 625*7=4375, 625*9=5625, 625*11=6875, 625*13=8125, and 625*15=9375.
Now take this list mod 16; since 625 = 1 mod 16 then the list is just the multipliers 3 through 15.
In order for a multiple of 16 to be consecutive one side or the other them the multiplier would be 1 or 15. That leaves exactly one option: 15. Then 625*15=9375 and 9375+1=9376=16*586. DEAL=9376.
Analytic Solution
