Brainsteem #6 Prize Maths Puzzle [Win 2SBD+1SBD]

Firstly, remember that there are TWO prizes, so anybody can win the random prize!

Slowly, slowly, let's start to make these Brainsteem Prize Maths Puzzles a bit tougher!

There are not many solutions, but you also need to prove that you have all of them.

Find all pairs of positive integers (n, k) such that n! = (n + 1)^k - 1.

image: designed myself

The Prizes

Earnings from each Brainsteem Puzzle will go towards the next Prizes.

For this Brainsteem # 5 the Prizes are:

2 SBD for the first correct answer that includes a valid method

1 SBD for one other correct answer that will be chosen randomly. That means you can still win this prize even if the answer may already be visible!

Please upvote! Resteem if you think this is a great puzzle! I will upvote all correct answers and any other interesting comments. To be fair to everyone, the prize closes after 7 days. Winners will be notified after that date and usernames posted with a solution.

Enjoy!

Brainsteem #6 Prize Maths Puzzle [Win 2SBD+1SBD]

Find all pairs of positive integers (n, k) such that n! = (n + 1)^k - 1.

The Prizes

Please upvote, resteem and follow @rycharde for more Brainsteem Prizes!

I try to upvote every interesting comment.

Steemit is not a zero-sum game!

Upvote each other and create the community you want to see!

Brainsteem #6 Prize Maths Puzzle [Win 2SBD+1SBD]

Find all pairs of positive integers (n, k) such that n! = (n + 1)k - 1.

The Prizes

Please upvote, resteem and follow @rycharde for more Brainsteem Prizes!

I try to upvote every interesting comment.

Steemit is not a zero-sum game!

Upvote each other and create the community you want to see!

Find all pairs of positive integers (n, k) such that n! = (n + 1)^k - 1.