Problem
NT-B1-M05-P020 A Symmetric Equation
#20
★★★☆☆ Level 3 of 5
Find all positive integer solutions of \(xy=4x+4y+5\).
Move \(4x+4y\) to the left and add \(16\).
From \(xy-4x-4y=5\), we get \((x-4)(y-4)=21\). The positive divisors of \(21\) are \(1,3,7,21\). This gives \((5,25)\), \((7,11)\), \((11,7)\), \((25,5)\). Negative factors do not give positive \(x,y\).
A good problem for checking all signs after factorisation.