Question

Aflati cel mai mic numar natural care, impartit la 56 da restul 53,impartit la 50 da restul 47,iar impartit la 21 da restul 18.

Answer 1

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