Sets, Relations & Functions
Counting n where 3^n-3 Divisible by 7
nta_pyq_2023_apr
Grade 11
Question:
The number of elements in $\{n\in\mathbb{N}:\ 10\leq n\leq100,\ 3^n-3\ \text{is a multiple of 7}\}$ is _______.
Step-by-Step Solution
Key Concept: $3^n\equiv3\pmod7$. $3^1\equiv3$, $3^7\equiv3\pmod7$ (period 6). So $n\equiv1\pmod6$.
15 elements.
Correct Answer: 15