Răspuns: 359 -> numarul
Explicație pas cu pas:
n : 12 = c₁ rest 11 ⇒ n = 12 × c₁ + 11 [ + 1 ⇒ n + 1 = 12 × ( c₁ + 1)
n : 18 = c₂ rest 17 ⇒ n = 18 × c₂ + 17 [ + 1 ⇒ n + 1 = 17 × ( c₂ + 1 )
n : 40 = c₃ rest 39 ⇒ n = 40 × c₃ + 39 l +1 ⇒ n + 1 = 40 × ( c₃ + 1 )
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=> n + 1 = c.m.m.m.c al numerelor 12, 18 si 40
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12 = 2² × 3
18 = 2 × 3²
40 = 2³ × 5
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n + 1 = 2³ × 3² × 5 = 8 × 9 × 5 = 360
n = 360 - 1
n = 359 → numarul natural care, impartit la fiecare dintre numerele 12, 18, si 40, dau resturile 11, 17 si 39
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Verific:
359 : 12 = 29 rest 11
359 : 18 = 19 rest 17
359 : 40 = 8 rest 39
