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Division of Powers

Show that
2903^{n} - 803^{n} - 464^{n} + 261^{n}
is divisible by 1897 for all n>0.
Can you find an example of this for smaller values?

A small one I found is:
8^{n} + 7^{n} - 3^{n} - 2^{n}
is divisible by 10 for all n>0.

Source: Reader Jimmy Chng Gim Hong, from Singapore.

Solution

Mail to Ken