chinese remainder theorem examples

What is the remainder when 2 1990 is divided by 1990?
Originally Answered: Find the remainder when 2^1990 is divided by 1990? Thanks for the A2A.
The answer is 1024.

Example: Solve the simultaneous congruences x ≡ 6 (mod 11), x ≡ 13 (mod 16), x ≡ 9 (mod 21), x ≡ 19 (mod 25). Solution: Since 11, 16, 21, and 25 are pairwise relatively prime, the Chinese Remainder Theorem tells us that there is a unique solution modulo m, where m = 11⋅16⋅21⋅25 = 92400.

PDF	The Chinese Remainder Theorem Then w1 w2

PDF	Math 127: Chinese Remainder Theorem Example 2. Find x such that 3x ? 6 (mod 12). Solution. Uh oh. This time we don't have a multiplicative inverse to

PDF	Chinese Reminder Theorem The Chinese Remainder Theorem enables one to solve simultaneous equations with respect For example in the first equation for y1

PDF	The Chinese Remainder Theorem For example 6 is relatively prime to 25

PDF	The Chinese Remainder Theorem 07-Jun-2014 The basic form is about a number n that divided by some divisors and leaves remainders. Page 4. Title. Definition. Example. Principle. More ...

PDF	General Secret Sharing Based on the Chinese Remainder Theorem Threshold cryptography (see for example

PDF	Compartmented Secret Sharing Based on the Chinese Remainder The Chinese remainder theorem has many applications in computer science (see for example

PDF	Remainder Theorem Definition And Example Remainder and Factor Theorems Precalculus Socratic. The Chinese Remainder. Theorem NRICH Millennium. In examples of polynomials determined by its factor

PDF	The Chinese Remainder Theorem Theorem. Let m and n be two Example: Solve the system of congruences x ? 1 (mod 7) x ? 3 (mod 10). Note that the hypotheses of the Chinese re- mainder theorem are satisfied in this

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PDF	The Chinese Remainder Theorem Example We solve the system 2x ≡ 5 (mod 7); 3x ≡ 4 (mod 8) of two linear congruences (in one variable x) Multiply the first congruence by 2-1 mod 7 = 4 to get 4 · 2x ≡ 4 · 5 (mod 7) This simplifies to x ≡ 6 (mod 7), so x = [6]7 or x =6+7t, where t ∈ Z

PDF	Math 127: Chinese Remainder Theorem Example 2 Find x such that 3x ≡ 6 (mod 12) Solution Uh oh This time we don't have a multiplicative inverse to

PDF	Chinese Remainder Theorem Example Find a solution to x ≡ 88 Chinese Remainder Theorem Example Find a solution to x ≡ 88 (mod 6) x ≡ 100 (mod 15) Solution 1: From the first equation we know we want x − 88 = 6k

PDF	The Chinese Remainder Theorem Lemma 1 Let m and a1, , an be positive integers If m is relatively prime to each of a1, , an, then it is relatively prime to their product a1 ··· an Proof If (m, a1 ···

PDF	Extending the Chinese Remainder Theorem Example Suppose we Extending the Chinese Remainder Theorem Example Suppose we have three congruences to solve simulatenously: (1) x ≡ 3 (mod 5) (2) x ≡ 7 (mod 8)

PDF	33 Chinese Remainder Theorem begin with a motivating example Example 3 3 1 Determine the smallest positive integer that gives a remain der of 2 upon division by 3, a remainder

PDF	The Chinese Remainder Theorem - UCSB Math 7 jui 2014 · The basic form is about a number n that divided by some divisors and leaves remainders Page 4 Title Definition Example Principle More

PDF	The Chinese Remainder Theorem 19 fév 2018 · Let a1,a2, ,an ∈ Z be pairwise relatively prime If b ∈ Z and aib for all i, then a1a2 ···anb Proof By induction on

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