Prove that for all integers n > 0, 10ⁿ⁺¹ + 10ⁿ + 1 is divisible by 3.

Basis step:

10 ⁿ⁺¹ + 10 ^{n +1} is divisible by 3

10 ¹⁺¹ + 10 ^{1 +1} is divisible by 3

10² + 10¹⁺¹ is divisible by 3

100 + 20 = 120

120/3 =40 therefore;

10² + 10¹⁺¹ is divisible by 3

induction step:

"Struggling here"