My Math Forum For what natural n is the number (5^(2*n+1))*(2^(n+2))+(3^(n+2))+(2^(2*n+1)) divisibl

 Number Theory Number Theory Math Forum

 July 1st, 2019, 07:39 AM #1 Newbie   Joined: Jun 2019 From: London Posts: 13 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) + (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.
 July 1st, 2019, 04:03 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,965 Thanks: 2214 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.

 Tags 12n, 22n, 52n, divisibl, math, natural, number, number theory

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post panky Algebra 4 May 20th, 2016 03:53 AM zylo Topology 13 February 18th, 2016 08:07 AM ManInTheSuit New Users 4 June 2nd, 2015 05:48 AM Shen Elementary Math 2 June 5th, 2014 07:50 AM johnny Calculus 3 March 7th, 2011 08:02 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top