Question

Determinati toate numerele de forma ''abc'', scrise in baza 10, astfel incat ''abc'' impartit la ''bc'' da catul 5 si restul 4.

Answer 1

abc=100a+10b+c
bc=10b+c
100a+10b+c=5(10b+c)+4
100a+10b+c=50b+5c+4
100a=(50b-10b)+(5c-c)+4
100a=40b+4c+4
4*25a=4*(10b+c+1)
25a=10b+c+1
10b+c+1≤100
25a≤100
a≠0
a∈{1;2;3;4}
a=1
10b+c=24
100a+10b+c=124
a=2
10b+c=49
100a+10b+c=249
a=3
10b+c=74
100a+10b+c=374
a=4
10b+c=99
100a+10b+c=499
,,abc"∈{124;249;374;499}
Proba:
124=24*5+4
249=49*5+4
374=74*5+4
499=99*5+4