Mock AIME 1 2007-2008 Problems/Problem 12
Problem 12
Let and . If , how many integral values of are there such that is a multiple of ?
Solution
(If you recall the reverse of Sophie Germain Identity with , then you could have directly found the answer).
By Fermat's Little Theorem, we have that if and if . Also, we note that by examining a couple of terms, if and if . Therefore, With divisibility by achievable only if . There are odd numbers in the range given, and of those are divisible by , so the answer is .
See also
Mock AIME 1 2007-2008 (Problems, Source) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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