notam m=√n²-2n+17=√n²-2n+1+16=√(n-1)²+16, m>0
ridicam la patrat
m²=(n-1)²+4²
(n-1)²-m²=-16
(n-1-m)(n-1+m)=-16
dar -16=-1*16=1*(-16)=-2*8=-8*2=-4*4
n-1-m<n-1+m
avem urmatoarele posibilitati
1) n-1-m=-1
n-1+m=16
n-m=0
n+m=17
le adunam si obtinem
2n=17 imposibil
2) n-1-m=-2
n-1+m=8
n-m=-1
n+m=9
=> 2n=8
* n=4
=>m=√9+16=5
3) n-1-m=-4
n-1+m=4
n-m=-3
n+m=5
2n=2
* n=1
m=√0+16=4 solutie buna
4) n-1-m=-8
n-1+m=2
n-m=-7
n+m=3
2n=-4
* n=-2
=> m=√(+16=5 solutie buna
5) n-1-m=-16
n-1+m=1
n-m=-15
n+m=2
2n=-13 imposibil
deci solutiile sunt n∈{-2,1,4}
O zi buna!
