n : 56 = c₁ rest 53 ⇒ n = 56 x c₁ + 53 l + 3 ⇒ n + 3 = 56 × ( c₁ + 1 )
n : 50 = c₂ rest 47 ⇒ n = 50 × c₂ + 47 l + 3 ⇒ n + 3 = 50 × ( c₂ + 1 )
n : 21 = c₃ rest 18 ⇒ n = 21 × c₃ + 18 l + 3 ⇒ n + 3 = 21 × ( c₃ + 1 )
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⇔ n + 3 = c.m.m.m.c al numerelor ( 56, 50, 21 )
56 = 2³ x 7
50 = 2 × 5²
21 = 3 × 7
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c.m.m.m.c al numerelor ( 56, 50 si 21 ) = 2³ × 3 × 5² × 7 = 4 200
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n + 3 = 4 200 ⇒ n = 4 200 - 3 ⇒ n = 4 197 → numarul
Verific:
4 197 : 56 = 74 rest 53
4 197 : 50 = 83 rest 47
4 197 : 21 = 199 rest 18
Raspuns: 4 197 → numarul natural
