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232 | 20^n + 16^n - 3^n - 1

Problem:
If \(n\) is even, then \( 323 | 20^n + 16^n - 3^n - 1 \).

Solution:
Let \( n = 2k \).
We have \( 17 | 400^k - 9^k \) and \( 17 | 256^k - 1 \). Hence \( 17 | 20^n + 16^n - 3^n - 1 \).
Also \( 19 | 20^n -1 \) and \( 19 | 256^k - 9^k \). Hence  \(19 | 20^n + 16^n - 3^n - 1 \).
Hence it is divisible by \( 17 \times 19 = 323 \). QED

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