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...
Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q6 Paid Members Public
My Solution for "Working modulo $9$ or $11$, find the missing digits in the calculations below: (a) $51840 \cdot 273581 = 1418243x040$. (b) $2x99561 = [3(523 + x)]^2$. (c) $2784x = x \cdot 5569$. (d) $512 \cdot 1x53125 = 1000000000$."
