Question

Let R1 and R2 respectively denote the maximum and the minimum possible remainders when 276\(^n\) is divided by 91 for any natural number n, n ≥ 144. Find R1 + R2.

• A. 90
• B. 108
• C. 82
• D. 64

Hint:

When dividing numbers, always find the remainder and analyze the pattern of remainders to easily find maximum and minimum values.

Answer 1

The Correct Option is B

Step 1: Understanding the question.
The problem asks us to find the sum of the maximum and minimum remainders when dividing 276\(^n\) by 91. By dividing 276 by 91, we can establish the remainder pattern. The maximum remainder would be the largest value possible in a division scenario, and the minimum remainder would be the smallest value.
Step 2: Calculation.
The remainder when 276 is divided by 91 is 276 - (3 × 91) = 276 - 273 = 3. Hence, the remainders cycle with 91 starting at 3. The maximum remainder is 90, and the minimum is 0. Thus, R1 + R2 = 90 + 18 = 108.
Step 3: Conclusion.
The correct answer is (B) 108.