Problem 4
Find all pairs of integers (m,n) such that m squared plus 4n and n squared plus 4m are both perfect squares.
Step 2 of 5: Find a small integer root
Detailed analysis
Because |x1x2|=|n|<=|m|=|x1+x2|, the two nonzero integer roots cannot both have absolute value at least 3. Hence one root has absolute value at most 2, so it is one of 1,-1,2,-2.