I have pairs, but I need to find an organzied method for finding them?
Hello, Rinnie!
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:
. .
Therefore: .