1. For how many n=2,3,4,...,99,100 is the base-n number 235236_n a multiple of 7?
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.
+118608 Write it properly and you might have a better chance of a timely answer.
Just edit it and take the $ signs away.
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.
