Matematické Fórum

Skrytý text:

(Assuming only non-negative integers)
Neither of or is equal to 1. So .
Now consider two cases:
1)
    WLOG
   
    if contradiction
    if contradiction
2)
    obviously and
    . Since and 2 isnt divisible by 3, then k isnt divisible by 3. But (consecutive integers) and neither of them can be divisible by 3, therefore k is product of 2 integers at most. So (for ) or .
For we get and .
For we get also contradiction.
To sum up: only solution .