11xQ+r=123
Dacă r<11 => r= {1,2,3,4,5,6,7,8,9,10}
1) r=1
11q=123-1
11q=122
q= 11,(09) (Fals)
2) r=2
11q=123-2
11q=121
q=11 (Adevărat)
3)r=3
11q=123-3
11q=120
q= 10, (90) (Fals)
4) r=4
11q=199
q= 18, (09) (Fals)
5) r=5
11q=198
q=18 (Adevărat)
6) r=6
11q=197
q=16, (90) (Fals)
Deci înseamnă că există 2 cazuri:
a) r=2 / q=11
b) r=5 / q=18