Consider the following statements:<br>I. 61 divides 107^{100}-76^{100}<br>II. 100 divides 67^{5}+33^{5}<br>Which of the statements given above is/are correct?
- A. I only
- B. II only
- C. Both I and II ✓
- D. Neither I nor II
Correct Answer: C. Both I and II
Explanation
For I: a^n - b^n is divisible by a+b when n is even. 107+76=183, and 183 = 61 \times 3, so 61 divides it (True). For II: a^n+b^n is divisible by a+b when n is odd. 67+33=100 (True).
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