Elementary Number Theory Problems 3.3 Solution (David M. Burton's 7th Edition) Paid Members Public
My solutions for Burton's Elementary Number Theory Problems 3.3 (7th Edition)
Elementary Number Theory Problems 3.3 Solution (David M. Burton's 7th Edition) - Q28 Paid Members Public
My Solution for "(a) If $n > 1$, show that $n!$ is never a perfect square. (b) Find the values of $n \geq 1$ for which $$n! + (n + 1)! + (n + 2)!$$ is a perfect square. [Hint: Note that $n! + (n + 1)! + (n + 2)! = n!(n + 2)^{2}$ .]"
Elementary Number Theory Problems 3.3 Solution (David M. Burton's 7th Edition) - Q27 Paid Members Public
My Solution for "Prove that for every $n \geq 2$ there exists a prime $p$ with $p \leq n < 2p$. [Hint: In the case where $n = 2k + 1$, then by the Bertrand conjecture there exists a prime $p$ such that $k < p < 2k$.]"
Elementary Number Theory Problems 3.3 Solution (David M. Burton's 7th Edition) - Q26 Paid Members Public
My Solution for "Verify the following: (a) There exist infinitely many primes ending in $33$, such as $233$, $433$, $733$, $1033, ....$ [Hint: Apply Dirichlet's theorem.] (b) There exist infinitely many primes that do not belong to any pair of twin primes.... "
Elementary Number Theory Problems 3.3 Solution (David M. Burton's 7th Edition) - Q25 Paid Members Public
My Solution for "Let $p_{n}$ denote the $n$th prime. For $n > 3$, show that $$p_{n} < p_{1} + p_{2} + \cdots + p_{n-1}$$ [Hint: Use induction and the Bertrand conjecture.]"
Elementary Number Theory Problems 3.3 Solution (David M. Burton's 7th Edition) - Q24 Paid Members Public
My Solution for "Determine all twin primes $p$ and $q = p + 2$ for which $pq - 2$ is also prime."
Elementary Number Theory Problems 3.3 Solution (David M. Burton's 7th Edition) - Q23 Paid Members Public
My Solution for "(a) The arithmetic mean of the twin primes $5$ and $7$ is the triangular number $6$. Are there any other twin primes with a triangular mean? (b) The arithmetic mean of the twin primes $3$ and $5$ is the perfect square $4$. Are there any other twin primes with a square mean? "
Elementary Number Theory Problems 3.3 Solution (David M. Burton's 7th Edition) - Q22 Paid Members Public
My Solution for "Show that $13$ is the largest prime that can divide two successive integers of the form $n^{2} + 3$."
