3 Congruence

Proof: Suppose a ? b mod n. Then by Theorem 3.3 b = a + nq. If a leaves the remainder r when divided by n

3 Congruence

Proof: Suppose a ? b mod n. Then by Theorem 3.3 b = a + nq. If a leaves the remainder r when divided by n

Congruences

If n is an integer then a is congruent to b modulo n if and only if a and b have the same remainder when divided by n. Proof. By the division algorithm

Math 110A Homework #2

First we notice that if p divides both a and b then p2 divides both a2 Prove that a ? b (mod n if and only if a and b have the same remainder mod n.

Solutions to Homework Set 3 (Solutions to Homework Problems

Prove that a ? b (mod n) if and only if a and b leave the same remainder when divided by n. Proof. ?. Suppose a ? b (mod n). Then by definition

selected solutions from homework #1 - UCLA Mathematics 110A

2 juil. 2010 If a ? c = nk for some integer k then a and c leave the same remainder when divided by n. Remember

Congruences

Proposition 3. Two integers a b are congruent mod n if and only if they have the same remainder when divided by n. Proof. First 

CHAPTER 5 Contrapositive Proof

exercises for this chapter asks you to show that if a ? b (mod n) then a and b have the same remainder when divided by n. Page 5. 106. Contrapositive Proof.

Congruences

Theorem 2. If n ? Zn> 1

Number Theory

18 mar. 2022 Proposition 5. a ? b (mod m) if and only if m

3 Congruence - New York University

Theorem 3 4If a bmodn then a and b leave the same remainder when divided by n Conversely if a and b leave the same remainder when divided by n then a bmodn Proof: Supposea bmodn Then by Theorem 3 3b=a+nq Ifaleaves the remainder rwhen divided bynwehavea=nQ+rwith 0 r

What is the remainder when n is divided by 4?

When an integer (n) is divided by 4 the remainder is 2, when the same integer is divided by 3, the remainder is 1. What could be the value of n?

When is a set formed by all remainders?

3. A set is formed by all remainders when the odd numbers between 8 and 800 are divided by 5. What is the mode of the set? (A) 0 (D) 3 (B) 1 (E) 4 (C) 2.

Why is a mod b not a remainder?

It is because a mod b isn't simply the remainder as returned by the operator '%'. See some examples: There are some other definitions in math and other implementations in computer science according to the programming language and the computer hardware. Please see Modulo operation from Wikipedia.