Question

a)Determinati toate numerele naturale care impartite la 7 dau catul 32
b)Determinati toate numerele naturale care impartite la 9 dau catul 103

Answer 1

a) x = 7 * 32 + rest
    x = 224 + rest
Restul poate fi 0, 1,2, 3, 4, 5, 6
x apartine { 224, 225, 226,227,228, 229, 230 }

b) y = 9 * 103 + rest
    y = 927 + rest
Restul poate fi 0, 1, 2, 3, 4, 5, 6, 7, 8
y apartine { 927, 928, 929, 930, 931, 932, 933,
934, 935 }

Answer 2

n = 32·7 + r =224 +r   r < 7  7∈{0,1,2,3,4,5,6} ⇒ n∈{224,225,226,227,228,229,230}
b) n = 103·9 +r = 927 +r       r < 9                        r∈{0,1,2,3,4,5,6,7,8}
 n∈{927,928,929,930,931,932,933,934,935}