Prove That There Are No Solutions in Positive Integers to the Equation

question 3

Essay

Prove that there are no solutions in positive integers to the equation x⁴ + y⁴ = 100.

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Definitions:

Neanderthals

An extinct species of human, closely related to modern humans, that lived in Europe and parts of Asia until approximately 40,000 years ago.

Hominin Tools

Tools made by hominins, ancestors of modern humans, used to aid in activities such as hunting, processing food, and constructing shelters.

Left Africa

Refers to the migration of Homo sapiens out of Africa approximately 60,000 to 80,000 years ago, leading to the eventual global distribution of humans.

Monophyletic

Describes a group of organisms that are classified in the same taxon and share a common ancestor.