Problem:
The number of triples of positive integers which satisfy the simultaneous equations
is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
From the second equation, , and is prime. Consequently, the two factors must be and . Since and are positive integers, . Hence one must have and . Upon substituting for and for into the first equation, it becomes a quadratic, , with solutions and . Both of these, and the corresponding values of and , satisfy both equations. Thus the solutions are and .