32. gcd(𝑎+𝑏,𝑎^2+𝑏^2 )=1𝑜𝑟 2 | gcd(𝑎+𝑏,𝑎^2−𝑎𝑏+𝑏^2 )=1 𝑜𝑟 3 | Problems 2.4 | question 4 | M. Burton
Автор: ACADEMY OF MATHEMATICAL SCIENCES
Загружено: 2025-11-03
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Elementary Number Theory by David M. Burton | Problems 2.4
Chapter#2 Divisibility Theory in the Integers
In this lecture I will discuss question number 4 (c) and 4(d) of problems 2.4. This question is related to properties of greatest common divisor (gcd). This question can be stated as
If gcd (𝑎,𝑏)=1 then show
1. gcd(𝑎+𝑏,𝑎^2+𝑏^2 )=1 𝑜𝑟 2
2.gcd(𝑎+𝑏,𝑎^2−𝑎𝑏+𝑏^2 )=1 𝑜𝑟 3
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