1. $n$ is a non-negative integer, and $3n+1, 5n+1$ are both perfect squares. Then $7n+3$ is:
( A ) must be a prime number
(B) must be a composite number
(C) must be a perfect square
(D) none of the above
-、1.(D).
Let $n=0, 3n+1=5n+1=1^{2}, 7n+3=3$ be prime numbers. Take $n=16, 3n+1=7^{2}, 5n+1=9^{2}, 7n+3=115$ as composite numbers.
However, 3 and 115 are not perfect squares.