# Math

## Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q1 Paid Members Public

My Solution for "Use the binary exponentiation algorithm to compute both $19^{53} \pmod {503}$ and $141^{47} \pmod {1537}$. "

## Basic Techniques for Solving Theory of Congruence Problems - 1 Paid Members Public

8 Basic Techniques for solving theory of congruence/Modular Arithmetic problems summarised from my solution on Chapter 4.2 Elementary Number Theory 7th Edition Problems (David M. Burton).

## Elementary Number Theory Problems 4.2 Solution (David M. Burton's 7th Edition) Paid Members Public

My solutions for Burton's Elementary Number Theory Problems 4.2 (7th Edition)

## Elementary Number Theory Problems 4.2 Solution (David M. Burton's 7th Edition) - Q18 Paid Members Public

My Solution for "If $a \equiv b \pmod {n_{1}}$ and $a \equiv c \pmod {n2}$, prove that $b \equiv c \pmod {n}$, where the integer $n = gcd(n_{1}, n_{2})$."

## Elementary Number Theory Problems 4.2 Solution (David M. Burton's 7th Edition) - Q17 Paid Members Public

My Solution for "Prove that whenever $ab \equiv cd \pmod {n}$ and $b \equiv d \pmod {n}$, with $gcd(b, n) = 1$, then $a \equiv c \pmod {n}$."

## Elementary Number Theory Problems 4.2 Solution (David M. Burton's 7th Edition) - Q16 Paid Members Public

My Solution for "Use the theory of congruences to verify that $$89 \mid 2^{44} - 1 \qquad \text{and} \qquad 97 \mid 2 ^{48} - 1$$"

## Elementary Number Theory Problems 4.2 Solution (David M. Burton's 7th Edition) - Q15 Paid Members Public

My Solution for "Establish that if $a$ is an odd integer, then for any $n \geq 1$$$a^{2^{n}} \equiv 1 \pmod {2^{n + 2}}$$ [Hint: Proceed by induction on $n$.]"

## Elementary Number Theory Problems 4.2 Solution (David M. Burton's 7th Edition) - Q14 Paid Members Public

My Solution for "Give an example to show that $a^{k} \equiv b^{k} \pmod {n}$ and $k \equiv j \pmod {n}$ need not imply that $a^{j} \equiv b^{j} \pmod {n}$."