27. If two positive integers $m$ and $n$, both bigger than 1 , satisfy the equation
$$
2005^{2}+m^{2}=2004^{2}+n^{2},
$$
find the value of $m+n$.
27 Ans: 211 .
Since $(m+n)(m-n)=4009=211 \times 19$ which is a product of primes. Hence $m+n=211$.