6121

6121 is a positive integer that follows 6120 and precedes 6122. In number theory, it is notable for being a prime number.

As a prime, 6121 has no positive divisors other than 1 and itself. It is odd and congruent to 1 modulo 4, a property that places it in the class of primes for which the sum-of-two-squares theorem applies.

Fermat’s theorem on sums of two squares guarantees that every prime congruent to 1 mod 4 can be written as a sum of two squares. For 6121, one such representation is 6121 = 64^2 + 45^2. This expresses 6121 as the sum of two integer squares, and for primes of this form the representation is unique up to order and sign (that is, aside from swapping the squares or changing signs, there are no other distinct pairs).

In summary, 6121 is a prime number with a canonical expression as 64^2 + 45^2, illustrating a concrete instance of the two-squares theorem.

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