[PDF] a^k is congruent to b^k mod n

  • What does a ? b mod n mean?

    For a positive integer n, two integers a and b are said to be congruent modulo n (or a is congruent to b modulo n), if a and b have the same remainder when divided by n (or equivalently if a ? b is divisible by n ). It can be expressed as a ? b mod n. n is called the modulus.

  • What does a ? b mod m mean?

    BASIC PROPERTIES OF CONGRUENCES. The letters a, b, c, d, k represent integers. The letters m, n represent positive integers. The notation a ? b (mod m) means that m divides a ? b. We then say that a is congruent to b modulo m.

  • How do you prove a is congruent to b mod m?

    Intuitive idea : If two numbers a and b leave the same remainder when divided by a third number m, then we say "a is congruent to b modulo m", and write a ? b ( mod m ).
  • Modulus congruence means that both numbers, 11 and 16 for example, have the same remainder after the same modular (mod 5 for example). 11 mod 5 has a remainder of 1. 11/5 = 2 R1.
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Problem Set 4 Solutions

22 fév. 2005 (i) a ? b (mod n) implies ak ? bk (mod n) for all k ? 0. Solution. We use induction. ... holds because both sides are congruent to 0.



CHAPITRE 3 : CONGRUENCES ET ARITHMÉTIQUE MODULAIRE

a ? 0 (mod n) ?? a = nk avec k entier. ?? a est un multiple de n. Quelques propriétés de la congruence. Théorème 1.2. Soit a b



Congruences and Modular Arithmetic

Let n ? N and ab ? Z. We say that a is congruent to b modulo n



DIVISIBILITÉ ET CONGRUENCES

a divise b s'il existe un entier relatif k tel que b = ka. Deux entiers a et b sont congrus modulo n lorsque a – b est divisible par n.



Congruences

We will say that two integers a and b are congruent modulo n and we write a ? b mod n If a ? b mod n



Number Theory

Integer a is congruent to integer b modulo m > 0 if a and b give If a ? b (mod m)



Congruences (Part 1)

"a is congruent to b modulo m" means m



Congruences (Part 1)

"a is congruent to b modulo m" means m



Number Theory Homework.

b)+(b ? a). D. We now show that congruence mod n plays well with the basic arithmetic ... ak ? bk mod n. Proof. This is just an easy induction on k.



Homework 2 Solutions:

(Hint: Most of the terms are congruent to 0.) (3) Show that if n

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