The number 199 can be written as m^2-n^2, where m, n are natural numbers (m \gt n). What is the value of mn?

Explanation

Since 199 is prime, m^2-n^2 = (m-n)(m+n) = 1 \times 199. This implies m-n = 1 and m+n = 199. Solving gives m=100 and n=99. Their product is mn = 100 \times 99 = 9900.

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