Prove the following statement: if p and p+2 are twin primes and p > 5, then p³ +3p²-p-3=0 (mod 10). Hint: The product of any k consecutive integers is divisible by k. Alternatively, think what are possible values of p rem 2 and p rem 5.

Prove the following statement: if p and p+2 are twin primes and p > 5, then p³ +3p²-p-3=0 (mod 10). Hint: The product of any k consecutive integers is divisible by k. Alternatively, think what are possible values of p rem 2 and p rem 5.

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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Number theory is one of the most appealing topics in mathematics. Given one or more numeric values, a numeric algorithm performs some computation. The use of number theory in computing is important for applications like in the case of cryptographic algorithms. Number theory is also used in various applications such as calculating hash functions or in information security. Euclid’s algorithm is one of the oldest number-theoretic algorithms which is used to calculate the greatest common divisor of two numbers.

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Prove the following statement: if p and p+2 are twin primes and p > 5, then p³ +3p²-p-3=0 (mod 10).
Hint: The product of any k consecutive integers is divisible by k.
Alternatively, think what are possible values of p rem 2 and p rem 5.

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