Fie a-1=c
b-2=d
2*3²*5^6 *c*d patrat perfect si cub perfect
5^6 este p.p si c.p
ramane ca a-1=2^5.....a=2^5+1=32+1=33
si b-2=3^4.....b=3^4+2=81+2=83
incercam si permutandu-le
a-1=3^4...a=81+1=82
b-2=2^5...b=2^5+2=34
[problema admite 2 solutii , cand a e mai mic, b e mai mare si reciproc, dar a+b=116 constant
