Composite divisors 1

Number Theory Level 5

Amongst all the integers $n$ such that $n$ $\mid$ $2^{n}-2$ and $n$ $\mid$ $3^{n}-3$ ; Find the sum of the smallest two composite integers.

Also Try Part-2

The answer is 1666.

1 solution

Rishabh Tiwari
Jun 12, 2016

@Pi Han Goh , @Arturo Presa , @Calvin Lin @Sandeep Bhardwaj , @Brian Charlesworth , @Otto Bretscher , anyone? please help out to solve this problem ..thanking you in advance.

@Rishabh Tiwari , Do you mean that you had posted this problem. But, do not know how to solve it?

Janardhanan Sivaramakrishnan - 5 years ago

I do know a logical solution, but don't know how to solve it step by step as I am a beginner in Number theory , hence posted it so that I can learn from fellow brilliantians. As of now no one has provided a good solution ; Can you please provide a solution sir ? Thanking you in advance!

Rishabh Tiwari - 5 years ago

I am not one of the listed names, but Carmichael numbers satisfy Fermat's little theorem despite not being prime so we just sum the first two: 561+1105=1666.

Sal Gard - 5 years ago

@Sal Gard – Sorry, but as i said everyone is free to suggest & solve This question. But is there a proof ?

Rishabh Tiwari - 5 years ago

@Sal Gard – Indeed, the solution would involve Carmichael numbers. But, they need to be co-prime with both $2$ and $3$ . $561$ divides $3$ . This makes it difficult to confirm if the solution should be $561+1105=1666$ or $1105+1729=2834$ .

Janardhanan Sivaramakrishnan - 5 years ago

Composite divisors 1

The answer is 1666.

1 solution

0 pending reports