Question

Determinati numerele naturale n si a stiind ca 3^n+4+3^n+3+3^n+1=aaa

Answer 1

3ⁿ⁺⁴ + 3ⁿ⁺³ + 3ⁿ⁺¹ = aaa

3ⁿ⁺¹(3³ + 3² + 1) = aaa

3ⁿ⁺¹(27 + 9 + 1) = aaa

3ⁿ⁺¹ₓ37 = aaa

aaa poate fi 111, 222, 333, 444, 555, 666, 777, 888, 999

1)

3ⁿ⁺¹ₓ37 = 111

3ⁿ⁺¹ = 111 : 37

3ⁿ⁺¹ = 3¹

n + 1 = 1 => n = 0

2)

3ⁿ⁺¹ₓ37 = 222

3ⁿ⁺¹ = 6 nu ne convine

3)

3ⁿ⁺¹ₓ37 = 333

3ⁿ⁺¹ = 9

3ⁿ⁺¹ = 3²

n + 1 = 2 => n = 1

4)

3ⁿ⁺¹ₓ37 = 444

3ⁿ⁺¹ = 12 nu ne convine

5)

3ⁿ⁺¹ₓ37 = 555

3ⁿ⁺¹ = 15 nu ne convine

6)

3ⁿ⁺¹ₓ37 = 666

3ⁿ⁺¹ = 18 nu ne convine

7)

3ⁿ⁺¹ₓ37 = 777

3ⁿ⁺¹ = 21 nu ne convine

8)

3ⁿ⁺¹ₓ37 = 888

3ⁿ⁺¹ = 24 nu ne convine

9)

3ⁿ⁺¹ₓ37 = 999

3ⁿ⁺¹ = 27

3ⁿ⁺¹ = 3³

n + 1 = 3 => n = 2