Question

2. For example, let $q=p+2$ for $p$ and $q$ primes (i.e. $p$ and $q$ twin primes). Show that for an integer $a$ that fulfills the condition $p \mid a^2-q$ to exist, it is necessary and sufficient that an integer $b$ that fulfills the condition $q \mid b^2-p$ exists.

Name: 2. For example, let q=p+2 for p and q primes (i.e. p and q twin primes). Show that for an integer a that fulfills the condition p | a^2-q to exist, it is necessary and sufficient that an integer b that fulfills the condition q | b^2-p exists.
Uploaded: 2022-08-28T18:04:36-08:00
Duration: 1 min 45 s
Channel: Nick Johnson
Description: 2. For example, let q=p+2 for p and q primes (i.e. p and q twin primes). Show that for an integer a that fulfills the condition p | a^2-q to exist, it is necessary and sufficient that an integer b that fulfills the condition q | b^2-p exists.

          2. For example, let $q=p+2$ for $p$ and $q$ primes (i.e. $p$ and $q$ twin primes). Show that for an integer $a$ that fulfills the condition $p \mid a^2-q$ to exist, it is necessary and sufficient that an integer $b$ that fulfills the condition $q \mid b^2-p$ exists.

2. For example, let q=p+2 for p and q primes (i.e. p and q twin primes). Show that for an integer a that fulfills the condition p | a^2-q to exist, it is necessary and sufficient that an integer b that fulfills the condition q | b^2-p exists.

Added by Brian A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Nick Johnson

08/28/2022

Step 1

Step 1: Assume that there exists an integer $a$ such that $p \mid a^2 - q$. Show more…

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2. For example, let $q = p + 2$ for $p$ and $q$ primes (i.e. $p$ and $q$ are twin primes). Show that for an integer $a$ that fulfills the condition $p mid a^2 - q$ to exist, it is necessary and sufficient that an integer $b$ that fulfills the condition $p mid b^2 - p$ exists.