Fermat's Last Theorem: Principles

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FLT principles overview

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Жанерке Кенес

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Froggy Jumps Fermat's Last Theorem: PrinciplesVersión en línea FLT principles overview por Жанерке Кенес 1 What are principles in teaching? a It holds only for n=3 and n=5 b There exist infinitely many solutions for all n>2 c No three positive integers a, b, c satisfy a^n + b^n = c^n 2 Who proved Fermat's Last Theorem? a Leonhard Euler b Pierre de Fermat c Andrew Wiles (with Richard Taylor) 3 What mathematical objects are central to Wiles' proof? a Elliptic curves and modular forms b Matrices and vectors c Polynomials in one variable 4 Which classical method did Fermat originally try to use for FLT? a Infinite descent b Group theory c Calculus of variations 5 What is the Modularity Theorem related to FLT? a Every rational elliptic curve is modular b Every integer is modular c Every polynomial is modular 6 Is FLT known to be true for n=3? a Only for special a,b b Yes, no nontrivial positive integer solutions exist c No, there are solutions for n=3 7 What is a 'trivial solution' context for a^n + b^n = c^n? a When a=b=c b When a=0 or b=0 c When n is even 8 In Wiles’ proof, what is the role of the Taniyama-Shimura conjecture? a Bridge between semistable elliptic curves and modular forms b It proves FLT directly c It provides a numerical solution 9 What is an elliptic curve in this context? a A hyperbola family b A straight line in the plane c A cubic curve y^2 = x^3 + ax + b 10 In what year was FLT finally proven? a 1887 b 1994 c 1976

Froggy Jumps

Fermat's Last Theorem: PrinciplesVersión en línea

FLT principles overview

por Жанерке Кенес

What are principles in teaching?

It holds only for n=3 and n=5

There exist infinitely many solutions for all n>2

No three positive integers a, b, c satisfy a^n + b^n = c^n

Who proved Fermat's Last Theorem?

Leonhard Euler

Pierre de Fermat

Andrew Wiles (with Richard Taylor)

What mathematical objects are central to Wiles' proof?

Elliptic curves and modular forms

Matrices and vectors

Polynomials in one variable

Which classical method did Fermat originally try to use for FLT?

Infinite descent

Group theory

Calculus of variations

What is the Modularity Theorem related to FLT?

Every rational elliptic curve is modular

Every integer is modular

Every polynomial is modular

Is FLT known to be true for n=3?

Only for special a,b

Yes, no nontrivial positive integer solutions exist

No, there are solutions for n=3

What is a 'trivial solution' context for a^n + b^n = c^n?

When a=b=c

When a=0 or b=0

When n is even

In Wiles’ proof, what is the role of the Taniyama-Shimura conjecture?

Bridge between semistable elliptic curves and modular forms

It proves FLT directly

It provides a numerical solution

What is an elliptic curve in this context?

A hyperbola family

A straight line in the plane

A cubic curve y^2 = x^3 + ax + b

In what year was FLT finally proven?

1887

1994

1976

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Fermat's Last Theorem: Principles

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Creada por

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Fermat's Last Theorem: PrinciplesVersión en línea

por Жанерке Кенес

What are principles in teaching?

Who proved Fermat's Last Theorem?

What mathematical objects are central to Wiles' proof?

Which classical method did Fermat originally try to use for FLT?

What is the Modularity Theorem related to FLT?

Is FLT known to be true for n=3?

What is a 'trivial solution' context for a^n + b^n = c^n?

In Wiles’ proof, what is the role of the Taniyama-Shimura conjecture?

What is an elliptic curve in this context?

In what year was FLT finally proven?

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