Suppose that you want to calculate 1434661 · 3785648743 − 100020304 · 54300201. You are told that the answer is a positive integer less than 90. Compute the answer mod 10 and mod 9, then combine to get the answer. Show all the necessary work to obtain your answers. Note: This technique has often been employed to do calculations with large integers because most of the computations use small integers, with only the Chinese Remainder Theorem step requiring large integers. For example, if the answer is known to be less than 1036, the calculations can be done mod p for each prime less than 100. Since the product of the primes less than 100 is approximately 2.3 × 1036, the Chinese Remainder Theorem gives the answer exactly
Suppose that you want to calculate 1434661 · 3785648743 − 100020304 · 54300201. You are told that the answer is a positive integer less than 90. Compute the answer mod 10 and mod 9, then combine to get the answer. Show all the necessary work to obtain your answers. Note: This technique has often been employed to do calculations with large integers because most of the computations use small integers, with only the Chinese Remainder Theorem step requiring large integers. For example, if the answer is known to be less than 1036, the calculations can be done mod p for each prime less than 100. Since the product of the primes less than 100 is approximately 2.3 × 1036, the Chinese Remainder Theorem gives the answer exactly
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Suppose that you want to calculate 1434661 · 3785648743 − 100020304 · 54300201. You are told that
the answer is a positive integer less than 90. Compute the answer mod 10 and mod 9, then combine
to get the answer. Show all the necessary work to obtain your answers. Note: This technique has
often been employed to do calculations with large integers because most of the computations use small
integers, with only the Chinese Remainder Theorem step requiring large integers. For example, if the
answer is known to be less than 1036, the calculations can be done mod p for each prime less than
100. Since the product of the primes less than 100 is approximately 2.3 × 1036, the Chinese Remainder
Theorem gives the answer exactly
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