2023 · Q32
The number 97³⁰ - 14³⁰ is divisible by :
Elementary MathematicsNumber System
- A37 but not 83
- B83 but not 37
- CBoth 37 and 83
- DNeither 37 nor 83
Explanation
97³⁰ − 14³⁰ is divisible by 97 − 14 = 83, since a^n − b^n is always divisible by a − b. Because the exponent 30 is even, it is also divisible by 97 + 14 = 111 = 3 × 37. Hence it is divisible by both 37 and 83 (C).