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Problem 282

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The Ackermann function

For non-negative integers m, n, the Ackermann function A(m, n) is defined as follows:

For example A(1, 0) = 2, A(2, 2) = 7 and A(3, 4) = 125.

Find ${\mathrm{\Sigma }}_{n=0}^{6}A(n,n)$ and give your answer mod 14⁸.

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阿克曼函数

对于非负整数m和n，阿克曼函数A(m, n)按如下方式定义：

例如，A(1, 0) = 2，A(2, 2) = 7，以及A(3, 4) = 125。

求${\mathrm{\Sigma }}_{n=0}^{6}A(n,n)$，并将你的答案模14⁸取余。

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