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. 6
• B. 20
• C. 15
• D. 32
• E. 34

Answer 1

The correct option is E 34

Option (e)

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