9719

9719 is a natural number that follows 9718 and precedes 9720. In mathematics, 9719 is a prime number, so its positive divisors are only 1 and 9719. It is odd and, more specifically, congruent to 3 modulo 4 (9719 ≡ 3 mod 4).

Several number-theoretic consequences follow from this classification. Primes congruent to 3 modulo 4 cannot be expressed as a sum of two squares, so 9719 cannot be written in the form x^2 + y^2 with integers x and y. Legendre’s three-square theorem further implies that 9719 cannot be represented as a sum of three squares, since it is congruent to 7 modulo 8 (9719 ≡ 7 mod 8). By contrast, Lagrange’s four-square theorem guarantees that every natural number, including 9719, can be written as a sum of four integer squares, though that representation is not unique and is not specified here.

In decimal form, 9719 consists of the digits 9, 7, 1, and 9; the number is not a palindrome since reversing the digits yields 9179. Beyond its basic arithmetic properties, 9719 is typically treated as a plain integer in numerical contexts and does not have widely recognized special significance in standard references.