Kvant Math Problem 849

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Verified: no
Verdicts: SKIP + SKIP
Solve time: 15m44s
Source on kvant.digital

Problem

Using the digits 1, 2, $\ldots$, 7, arranged in different orders, seven seven-digit numbers are formed. Prove that the sum of the seventh powers of some of these numbers cannot equal the sum of the seventh powers of the remaining numbers.

G. A. Galperin