Too much recursion
The Ackermann function is defined as
A ( m , n ) = ⎩ ⎪ ⎨ ⎪ ⎧ n + 1 A ( m − 1 , 1 ) A ( m − 1 , A ( m , n − 1 ) ) if m = 0 if m > 0 and n = 0 if m > 0 and n > 0 .
For all integers n > 1 , the value of A ( 4 , n ) all have the same remainder when divided by 1000. What is this remainder?
The answer is 733.
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1 solution
You need to show that A ( 4 , 2 ) ≡ A ( 4 , 3 ) ≡ A ( 4 , 4 ) ≡ A ( 4 , 5 ) ≡ … ≡ 7 3 3 ( m o d 1 0 0 0 ) .
The function A ( 4 , n ) cannot be computed for n > 2 in one's lifetime. However, A ( 4 , 2 ) = 2 0 0 3 5 2 9 9 3 0 . . . . 5 6 7 3 3