Find at least one pair of natural numbers (a, b) such that a^2 - b^2 = 48397?

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Mohammad Hassan Abbaspour

A perfect answer. Thanks.

Meanwhile, I found that my favorite number (48397) is a prime number and the next two primes (48407 and 48409) are twin primes.

Nebi Caka

a^2 – b^2 = (a-b)(a+b) = 48397

For: a – b = 1 →

a + b = 2a – 1 = 48397 →

a = 48398/2 = 24199, b = a – 1 = 24198