1994 AJHSME Problems/Problem 10
Contents
[hide]Problem
For how many positive integer values of is the expression an integer?
Solution
We should list all the positive divisors of and count them. By trial and error, the divisors of are found to be , for a total of . However, and can't be equal to for a POSITIVE integer N, so the number of possibilities is .
Solution 2
To find the number of positive divisors of , first prime factorize to get . Then add to the power of both and to get . Multiply to get . Since the problem is asking only for positive integer values of N, subtract from (since and result in integers that are not positive) to get .
~ spoamath321
See Also
1994 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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