2024 · Q96
The number 199 can be written as m² − n², where m, n are natural numbers (m > n). What is the value of mn?
Elementary MathematicsNumber System
- A9900
- B9800
- C9701
- DCannot be uniquely determined
Explanation
199 = m² − n² = (m−n)(m+n) with m > n natural. Since 199 is prime, the only factorization is 1 × 199, so m−n = 1 and m+n = 199. Solving gives m = 100, n = 99, and mn = 9900 — option A.