The number 97^{30}-14^{30} is divisible by :

  1. A. 37 but not 83
  2. B. 83 but not 37
  3. C. Both 37 and 83 ✓
  4. D. Neither 37 nor 83

Correct Answer: C. Both 37 and 83

Explanation

Using the property that x^n - y^n is divisible by both (x-y) and (x+y) when n is even. Here, (97-14) = 83 and (97+14) = 111. Since 111 = 3 \times 37, the expression is perfectly divisible by both 37 and 83.

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