Every integer can be written as the sum of 2 squares.

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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Exhibit the structure of the following statements by transforming them into a first-order formula,
indicating the interpretation of predicates and the domain. For example the statement There is
no greatest integer can be transformed into ¬∃x, ∀y, P(x, y) where P(x, y) is the predicate x ≥ y,
the domain being the integers.
Do not try to prove them (it may not be possible!).
1. Every integer can be written as the sum of 2 squares.
2. Every positive real number has a square root.
3. The cosine function has zeroes.
4. The cosine function has at least two distinct zeroes.
5. There is a neutral element1
for multiplication in real numbers.
6. Every odd square can be written as the sum of three odd numbers. 

 

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