p-2-2027-q-2-p-q-

Question Number 90013 by ar247 last updated on 20/Apr/20

- p^{2} + 2027 = - q^{2}

p + q = ?

Commented by mr W last updated on 21/Apr/20

p^{2} - q^{2} = 2027 \leftarrow p r i m e

(p - q) (p + q) = 1 \times 2027

f o r p, q \in N

p + q = 2027

p - q = 1

\Rightarrow p = 1014, q = 1013

Commented by MJS last updated on 21/Apr/20

for your solution, u = \frac{2027}{2}

Answered by MJS last updated on 21/Apr/20

p^{2} - q^{2} - 2027 = 0

p = u - v \land q = u + v

- 4 u v - 2027 = 0

v = - \frac{2027}{4 u}

p = u + \frac{2027}{4 u} \land q = u - \frac{2027}{4 u}

p + q = 2 u with u \neq 0

\Rightarrow p + q = z; z \in C ∖ {0}

Facebook Tweet Pin