1983 AHSME Problems/Problem 3
Problem 3
Three primes , and satisfy and . Then equals
Solution
We are given that and are primes. In order for and to sum to another prime, either or has to be even, because the sum of two odd numbers would be even, and the only even prime is (but would have, as the only solution in positive integers, , and is not prime). Thus, with one of either or being even, either or must be , and as , we deduce (as is the smallest prime). This means the answer is .
See Also
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