Răspuns:
n = 8
Explicație pas cu pas:
3¹×3²×3³×........×3ⁿ - (3²)¹⁷ = 8x9¹⁷ <=>
3¹×3²×3³×........×3ⁿ = 3²ˣ¹⁷ + 8×3²ˣ¹⁷ <=>
3¹×3²×3³×........×3ⁿ = 3³⁴×(1+8) <=>
3¹×3²×3³×........×3ⁿ =3³⁴×9 = 3³⁴×3² = 3³⁴+² = 3³⁶
3¹×3²×3³×........×3ⁿ = 3³⁶ <=>
3¹⁺²⁺³⁺······⁺ⁿ = 3³⁶ =>
1+2+3+.....+n = 36
n(n+1):2 = 36 => n(n+1) = 72
(produs de doua numere consecutive)
72 = 8x9 => n = 8
