thus m-n, or m+n must equal one of the divisors of 400, to satisfy the equation, and so that m,n will be positive integers.
for example, 10 is a divisor of 400:
m - n = 10
m + n = 40
-> m = 25, n = 15
Find all pairs of positive integers whose squares differ by 400.
Let be positive integers such that: .
Then we have: . ... where
Solve the system: .
Since are integers, have the same parity;
. . both even or both odd.
The only ways to factor 400 into two factors with the same parity are:
Then we have: