2007 iTest Problems/Problem 14
Problem
Let be the number of positive integers which are relatively prime to . For how many distinct values of is ?
Solution
If then . Hence every prime factor of is contained in . Let be the largest prime dividing . If then . If then with giving solutions . If then with , no solutions since is always even unless it is 1. Otherwise where and . Hence . Therefore all solutions are given by and the answer is G.
~Solution by Alexheinis but not posted on the wiki by Alexhienis
See Also
2007 iTest (Problems, Answer Key) | ||
Preceded by: Problem 13 |
Followed by: Problem 15 | |
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