求助一道prep的数学PS题

If P and n are positive integers and p>n, what is the remainder when p^2-n^2  is divided by 15?

(1) The remainder when p+n is divided by 5 is 1

(2) The remainder when p-n is divided by 3 is 1

此题答案是 (1) 和（2）合起来也不能得出结论

关于这类余数的题我一直找不到解题思路，不知道该如何处理。。请大家指导一下！！

不甚感激~~~~~~

p^2-n^2=(p-n)(p+n)=15a+r,即r=(p-n)(p+n)-15a

conditon1:p-n=5b+1,conditon2:p+n=3c+1

结合这两个条件带进去：r=(5b+1)(3c+1）-15a，有这么多未知数你不知道。怎么算出来，所以是e