A Modular Problem for Aditya Kumar

Number Theory Level 4

Find the remainder when $9271^{1729}$ is divided by 1729.

The answer is 626.

2 solutions

Otto Bretscher
Apr 21, 2016

$\lambda(1729)=\lambda(7\times13\times19)=\gcd(6,12,18)=36$ so $626^{1729}=626^{48\times36+1}\equiv \boxed{626} \pmod{1729}$

I did the same...thanks for teaching me Carmichael Lambda function :)

A Former Brilliant Member - 5 years, 1 month ago

Which Aditya kumar is that?

Aditya Kumar - 5 years, 1 month ago

Why u told that which Aditya kr is that. Those both are same at all.

Ayush Kumar - 3 years, 3 months ago

Exact same method

Aditya Kumar - 5 years, 1 month ago

Can't we do it by fermats little theorem?

Ayush Kumar - 3 years, 3 months ago

no, because 1729 is not prime

Zuokang Qu - 1 year, 5 months ago

What does this lambda mean? Is it gama function? I didn't understand this method, I have simple done it with another theorem.

Ayush Kumar - 3 years, 3 months ago

It means the Carmichael's Lambda Function

Shreyansh Mukhopadhyay - 3 years, 3 months ago

Sean Elma
Sep 24, 2020

We note that 1729 is prime, and gcd(9271, 1729) is 1. That hints on fermats theorom. From FT we get that the answer is 9271 mo 1729 which is simply 626.

A Modular Problem for Aditya Kumar

The answer is 626.

2 solutions

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