SAT数学题目if n and p are intergers greater than 1 and if p is a

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SAT数学题目
if n and p are intergers greater than 1 and if p is a factor of both n+3.what is the value of p?
答案是 10 ,为什么?
这是原题！

楼主题目有错
题目：If n and p are integers greater than 1 and if p is a factor of both n +3 and n +10,what is the value of p
if p is a factor of n+3 and n+10 then;
p*x=n+3 and p*y=n+10 where x and y are natural numbers;
then; p*y-p*x=n+10 -(n+3) => p*(y-x)=7;
Since 7 has only two factors 1 and 7; p can either be 1 or 7.
Since p>1 p=7.

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