Question

The remainder of $\frac{k^6}{9}=1$. How many values are possible for k if k is a natural number less than 50?

• A. 20
• B. 15
• C. 32
• D. 34

Answer 1

The correct option is D 34

6 is the Euler’s number of 9. If you divide the 6th power of any number which is relatively prime to 9, the remainder will be 1. Answer = all numbers which are non-multiples of 3. There will be $\frac{50}{3}$ multiples of 3. Non-multiples of 3 = $50-16=34$, which is the answer.