Hats off to Sir Euler

Algebra Level 4

Find the number of ordered pairs of ( x , y ) (x,y) when x x and y y are coprime positive integers that satisfy 11592658 = x + y . 11592658=x+y.


The answer is 4516560.

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Mehul Chaturvedi by Mehul Chaturvedi , 22, India

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1 solution

Mehul Chaturvedi
Dec 20, 2014

Here we would use Euler's totient function

It gives us the no. of numbers coprime to a no. "M"

i.e φ M = \large{\varphi M=} No. of numbers coprime to M M

So φ 11592658 = 4516560 \large{\varphi 11592658=4516560}

The answer is

⇒ 4516560 \Rightarrow \quad \huge \boxed{{4516560}}

I would love to see any other method

2 Helpful 0 Interesting 0 Brilliant 0 Confused

No offense but I think that you should rephrase your question to mean that x and y are coprime and their sum represents number of numbers coprime to M .

Although I misinterpreted your question and solved it the right way , I may be wrong ?

Anyways, Happy New Year .

A Former Brilliant Member - 6 years, 5 months ago

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Why is this a level 5!!!

Parth Lohomi - 6 years, 4 months ago

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