n : 10 = a rest 9 => n = 10×a + 9 | +1
n : 9 = b rest 8 => n = 9 ×b + 8 | +1
=> n + 1 = 10 × ( a + 1)
=> n + 1 = 9 × ( b + 1)
n + 1 = cmmmc [ 10; 9 ]
n + 1 = 10 × 9
n + 1 = 90
n = 89 (numarul cautat)
____________________
89 : 10 = 8 rest 9
89 : 9 = 9 rest 8