Elementary Number Theory Problems 3.2 Solution (David M. Burton's 7th Edition) Paid Members Public
My solutions for Burton's Elementary Number Theory Problems 3.2 (7th Edition)
Elementary Number Theory Problems 3.2 Solution (David M. Burton's 7th Edition) - Q14 Paid Members Public
My Solution for "Use the previous problem to obtain the prime factors of the repunit $R10$."
Elementary Number Theory Problems 3.2 Solution (David M. Burton's 7th Edition) - Q13 Paid Members Public
My Solution for "For the repunits $R_{n}$, verify the assertions below: (a) If $n \mid m$, then $R_{n} \mid R_{m}$. (b) If $d \mid R_{n}$ and $d \mid R_{m}$, then $d \mid R_{n+m}$.[Hint: Show that $R_{m+n} = R_{n}10^{m} + R_{m}$.] (c) If $gcd(n, m) = 1$, then $gcd(R_{n}, R_{m})= 1$."
Elementary Number Theory Problems 3.2 Solution (David M. Burton's 7th Edition) - Q12 Paid Members Public
Assuming that $p_{n}$ is the $n$th prime number, prove:(a) $p_{n} > 2n - 1$ for $n \geq 5$.(b) None of the integers $P_{n} = p_{1}p_{2} \cdots p_{n} + 1$ is a perfect square. (c) The sum $\frac{1}{p_{1}} + \frac{1}{p_{2}} + \cdots + \frac{1}{p_{n}}$ is never an integer.
Elementary Number Theory Problems 3.2 Solution (David M. Burton's 7th Edition) - Q11 Paid Members Public
My Solution for "If $p_{n}$ denotes the $n$th prime number, put $d_{n} = p_{n+1} - p_{n}$. An open question is whether the equation $d_{n} = d_{n + 1}$ has infinitely many solutions. Give five solutions."
Elementary Number Theory Problems 3.2 Solution (David M. Burton's 7th Edition) - Q10 Paid Members Public
My Solution for "Let $q_{n}$ be the smallest prime that is strictly greater than $P_{n} = p_{1}p_{2} \cdots p_{n} + 1$. It has been conjectured that the difference $q_{n} - (p_{1}p_{2} \cdots p_{n})$ is always a prime. Confirm this for the first five values of $n$."
Elementary Number Theory Problems 3.2 Solution (David M. Burton's 7th Edition) - Q9 Paid Members Public
My Solution for "(a) Prove that if $n \gt 2$, then there exists a prime $p$ satisfying $n \lt p \lt n!$. (b) For $n \gt 1$, show that every prime divisor of $n! + 1$ is an odd integer that is greater than $n$."
Elementary Number Theory Problems 3.2 Solution (David M. Burton's 7th Edition) - Q8 Paid Members Public
My Solution for "Assume that there are only finitely many primes, say $p_{1}, p_{2}, ..., p_{n}$. Use the following integer to arrive at a contradiction: $N = p_{2}p_{3} \cdots p_{n} + p_{1}p_{3} \cdots p_{n} + \cdots + p_{1}p_{2} \cdots p_{n-1}$"
