## Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q10 Paid Members Public

My Solution for "Prove that no integer whose digits add up to $15$ can be a square or a cube. [Hint: For any $a$, $a^{3} \equiv 0$, $1$, or $8$ $\pmod 9$.]"

## All Solutions for Insomnia Sufferers - 4 Paid Members Public

My fourth article for solutions for insomnia. I want to share the various experiences I’ve gathered over many years in dealing with insomnia, covering both physiological and psychological aspects, and even a bit of occult.

## All Solutions for Insomnia Sufferers - 3 Paid Members Public

My third article for solutions for insomnia. I want to share the various experiences I’ve gathered over many years in dealing with insomnia, covering both physiological and psychological aspects, and even a bit of occult.

## All Solutions for Insomnia Sufferers - 2 Paid Members Public

My second article for solutions for insomnia. I want to share the various experiences I’ve gathered over many years in dealing with insomnia, covering both physiological and psychological aspects, and even a bit of occult.

## All Solutions for Insomnia Sufferers - 1 Paid Members Public

In this article, I want to share the various experiences I’ve gathered over many years in dealing with insomnia, covering both physiological and psychological aspects, and even a bit of occult.

## Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q9 Paid Members Public

My Solution for "Find the remainder when $4444^{4444}$ is divided by $9$. [Hint: Observe that $2^{3} \equiv -1 \pmod {9}$.]"

## Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q8 Paid Members Public

My Solution for "For any integer $a$, show that $a^2 - a + 7$ ends in one of the digits $3, 7$, or $9$."

## Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q7 Paid Members Public

Establish the following divisibility criteria: (a) An integer is divisible by $2$ if and only if its units digit is $0, 2, 4, 6,$ or $8$. (b) An integer is divisible by $3$ if and only if the sum of its digits is divisible by $3$. (c) An integer is divisible by $4$ if and only if the number...