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July 1st, 2019, 07:39 AM  #1 
Newbie Joined: Jun 2019 From: London Posts: 9 Thanks: 0  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) + (5019)(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. 
July 1st, 2019, 04:03 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,823 Thanks: 2160 
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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12n, 22n, 52n, divisibl, math, natural, number, number theory 
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