Question 466930
p a factor of n + 3 ==> n + 3 = rp, for some positive integer r

p a factor of n + 10 ==> n + 10 = sp, for some positive integer s

(n + 10 > n+ 3 ==> s > r.)

Hence (n+10) - (n+3) = sp - rp = (s-r)p, or (s-r)p = 7.  (Note that s-r is a positive integer.)

Hence  p divides the prime number 7 (divisors are 1 and 7.)

This means p = 7, since p > 1.