Răspuns:
( a, b) = ( 0, 130), ( 26, 104), ( 52, 78), ( 78, 52), ( 104, 26), (130, 0)
Explicație pas cu pas:
a + b = 130 → suma a două numere naturale
a : 26 = c₁ rest 0 ⇒ a = 26 × c₁
b : 26 = c₂ rest 0 ⇒ b = 26 × c₂
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a + b = 130
26 × c₁ + 26 × c₂ = 130
26 × ( c₁ + c₂ ) = 130
c₁ + c₂ = 130 : 26
c₁ + c₂ = 5
c₁ ∈ { 0, 1 , 2, 3, 4, 5 }
↓ ↓ ↓ ↓ ↓ ↓
c₂ ∈ {5, 4, 3, 2, 1, 0 }
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a = 26 × 0, = 26 × 1, = 26 × 2, = 26 × 3, = 26 × 4, = 26 × 5
b = 26 × 5, = 26 × 4, = 26 × 3, = 26 × 2, = 26 × 1, = 26 × 0
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a ∈ { 0, 26, 52, 78, 104, 130 }
b ∈ {130, 104, 78, 52, 26, 0}
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Verific:
a + b = 130
0 + 130 = 130
26 + 104 = 130
52 + 78 = 130
78 + 52 = 130
104+26 = 130
130 + 0 = 130
