\section*{Exercise 5 - V11225}

A four-digit number is sought that is equal to the fourth power of its cross sum.

How did you determine the number?
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Since the fourth power of the cross sum is supposed to be a four-digit number and \(5^{4} < 9999\) holds, the cross sum can only be 6, 7, 8, or 9. Furthermore, it holds that \(6^{4}=1296, 7^{4}=2401, 8^{4}=4096\) and \(9^{4}=6561\). The sought number is thus 2401 with the cross sum 7.