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July 1st, 2019, 07:39 AM   #1
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For what natural n is the number (5^(2*n+1))*(2^(n+2))+(3^(n+2))+(2^(2*n+1)) divisibl

For what natural n is the number (5^(2*n+1))*(2^(n+2))+(3^(n+2))+(2^(2*n+1)) divisible by 19? I get that (19*(50^n + 12^n) + (50-19)(50^n +....+19^n). So it means that n can be any natural number? Or I did some mistake there?

Last edited by skipjack; July 1st, 2019 at 03:57 PM.
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July 1st, 2019, 04:03 PM   #2
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You definitely made a mistake, as your parentheses aren't paired correctly. The original expression seems to be divisible by 19 for n = 12, 30, 48, etc.
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