Alice, Betty and Carol each chose two 2-digit semiprimes (products of exactly two primes each) whose difference was also a semiprime. In each of the three cases, the six primes going into the three semiprimes involved were all different. Also in each case, the sum of the two semiprimes was a perfect square.

Alice, Betty and Carol had different pairs of semiprimes, though there may have been repetition of any given semiprime. Alice and Betty had the same sum for their semiprimes, but Carol's sum was different.

What were Carol's two semiprimes?

Carol's two semiprimes were 74 and 95.
The difference and the sum of the two semiprimes 74 and 95 are the semiprime 21 and the perfect square 169 (13²) respectively.

Alice's and Betty's semiprime pairs were (35, 86) and (26, 95).
The difference and the sum of the two semiprimes 35 and 86 are the semiprime 51 and the perfect square 121 (11²) respectively. The difference and the sum of the two semiprimes 26 and 95 are the semiprime 69 and the perfect square 121 (11²) respectively.

Posted by Dej Mar on 2011-04-13 01:58:14