2006 iTest Problems/Problem 28
Problem
The largest prime factor of is greater than . Determine the remainder obtained when this prime factor is divided by .
Solution
Note that . This expression can be factored with difference of squares and sum/difference of cubes. Note that since are all less than , none of them are the wanted factors. The only option left is . By doing a prime check (or noting that if has factors larger than 5, then the largest prime factor of the original number can not be greater than ), we confirm that is the largest prime factor of . The remainder when is divided by is .
See Also
2006 iTest (Problems, Answer Key) | ||
Preceded by: Problem 27 |
Followed by: Problem 29 | |
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