Largest Possible value of $n$

Number Theory Level 2

Let $a,b,c$ and $n$ be positive integer satisfying $a^n + b^n= c^n$ .

Find the largest possible value of $n$ .

0 1 2 3 Infinity

1 solution

Srinivasa Gopal
Nov 16, 2017

Fermat's last theorm states that the Diaphontine's equation a power n + b power n = c power n where a,b,c,n are integers does not have a solution for n > 2. The case where n is equal to 2 reduces to the pythogoras theorm which has infinite solutions. Wolfram Mathematica

Can you tell me why this happens? :)

Md Zuhair - 3 years, 6 months ago

This is nothing but the Fermat's last theorem. The proof is beyond the scope of this discussion as this was an open unproved problem for several centuries after Fermat had stated it sometime during the 17th century. It was solved recently by Andrew Wiles. I can share a wiki link as the proof involves elliptic groups and rings etc.,it is too complex and so your question "Why" has very complex proofs as its answer. Just feel free to browse through this wiki article. https://en.wikipedia.org/wiki/Fermat%27s Last Theorem

Srinivasa Gopal - 3 years, 6 months ago

Largest Possible value of n n n

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Largest Possible value of $n$