2008 iTest Problems/Problem 4
Contents
Problem
The difference between two prime numbers is . Find their sum.
Solution
We know that any prime number, excluding , is congruent to . Thus, if both of the primes are not , their difference would be congruent to . Because , one of the primes must be . It follows that the other prime must then be . Therefore, the sum of the two is .
Solution 2
Since the difference is , one number must be even for the difference to be even. is the only even prime number, and therefore is one of the two numbers. The other number is , and their sum: .
See Also
2008 iTest (Problems) | ||
Preceded by: Problem 3 |
Followed by: Problem 5 | |
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