Răspuns
Explicație pas cu pas:
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ab + ba = 10 a + b + 10 b + a = 11 a + 11 b = 11 × ( a + b ) → divizibil cu 11
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X = a x a²x a³ x ....... x²⁰⁰
X = a ⁽ ¹ ⁺ ² ⁺ ³ ⁺...... ⁺ ²⁰⁰ ⁾
1 + 2 + 3 + .... + 200 = 200 x ( 1 + 200 ) : 2 = 100 x 201 = 20 100
X = a²⁰¹⁰⁰
Y = ( a¹⁰⁰ )²⁰¹ = a²⁰¹⁰⁰
=> X = Y ; a²⁰¹⁰⁰ = a²⁰¹⁰⁰
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a + b = 340
a : ( b : 2 ) = 3 rest 25
a = 3 × ( b / 2 ) + 25
a = 3 b / 2 + 25
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a + b = 340
3 b / 2 + 25 + b = 340
3 b / 2 + b = 340 - 25
3 b + 2 b = 2 × 315
5 b = 630
b = 630 : 5 ⇒ b = 126 → numarul mic
a = 340 - 126 ⇒ a = 214 → numarul mare
Verific:
214 + 126 = 340 → suma celor doua numere
214 : ( 126 : 2 ) = 214 : 63 = 3 rest 25
