Problem:
How many ordered triples of integers satisfy the system of equations below?
Answer Choices:
A.
B.
C.
D. a finite number greater than two
E. infinitely many
Solution:
Adding the given equations and rearranging the terms of the resulting equation yields
or
Since a perfect square can only have or as a remainder when divided by , the sum of two perfect squares can only have or as a remainder when divided by , and hence the left and right sides of the above equation cannot be equal. There are no solutions.