Răspuns: 859
Explicație pas cu pas:
n : 32 = c₁ reest 27 ⇒ n = 32 × c₁ + 27 ║ adug 5 ⇒ n + 5 = 32×c₁ + 32
⇔ n + 5 = 32 × ( c₁+1) ( relaţia 1)
n : 48 = c₂ rest 43 ⇒ n = 48 × c₂ + 43 ║ + 5 ⇔ n + 5 = 48 × ( c₂ + 1 ) ( 2)
n : 54 = c₃ rest 49 ⇒ n = 54 × c₃ + 49 ║ + 5 ⇔ n + 5 = 54 × ( c₃ + 1 ) ( 3)
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⇔ n + 5 = c.m.m.m.c al numerelor 32, 48 şi 54
c.m.m.m.c cel mai mic multiplu comun
32 = 2⁵
48 = 2⁴x3
54 = 2x3³
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c.m.m.m.c al numerelor 32, 48 şi 54 = 2⁵ x 3³ = 32 x 27 = 864
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n + 5 = 864
n = 864 - 5
n = 859
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Verific:
859 : 32 = 26 rest 27
859 : 48 = 17 rest 43
859 : 54 = 15 rest 49
