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1. For how many n=2,3,4,...,99,100 is the base-n number 235236_n a multiple of 7?

 Feb 1, 2019
edited by Guest  Feb 1, 2019

Best Answer 

 #2
avatar
+1

If I understand your question:
This is the "closed form" of each term:
a_n = 1/2 (6 n + (-1)^(n + 1) + 13). 
And the number 235236(n) is a multiple of 7 in the following bases:
n = 10, 12, 16, 18, 22, 24, 28, 30, 34, 36, 40, 42, 46, 48, 52, 54, 58, 60, 64, 66, 70, 72, 76, 78, 82, 84, 88, 90, 94, 96, 100.

 Feb 1, 2019
 #1
avatar+96956 
+1

Write it properly and you might have a better chance of a timely answer.

Just edit it and take the $ signs away.

 Feb 1, 2019
 #2
avatar
+1
Best Answer

If I understand your question:
This is the "closed form" of each term:
a_n = 1/2 (6 n + (-1)^(n + 1) + 13). 
And the number 235236(n) is a multiple of 7 in the following bases:
n = 10, 12, 16, 18, 22, 24, 28, 30, 34, 36, 40, 42, 46, 48, 52, 54, 58, 60, 64, 66, 70, 72, 76, 78, 82, 84, 88, 90, 94, 96, 100.

Guest Feb 1, 2019

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