[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 279

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I have no idea how to approach it yet. I have to go through her with my heart.

I hope by "any few" you mean no more than five.

 

31,

331,

3331,

33331,

333331.

Check...! ;)

 

I had a similar idea, but I was trying to combine numbers like 2^k - 1. Let's check it out.

 
MetaDriver >>:

Проверяй..! ;)

Any pair is divisible by 2

any three is divisible by 3

any four is a four

and all five of them add up to five.

Mutual simplicity - checked in Excel, if anything, claims to Melkosoft :) :)

 

The only doubt is on 4. And about mutual simplicity, of course.

So, each successive one is the previous one multiplied by

 
Mathemat >>:

У меня похожая идейка была, тока я пытался комбинировать числа вида 2^k - 1. Ща проверим.

The main problem I had was the divisibility by three. Then I figured out how to construct it.

Of course, this is far from the claim of uniqueness of the solution.

 
Mathemat >>:

Единственное, в чем сомнения, - это на 4. И насчет взаимной простоты, конечно.

Four is easy - all digits greater than a hundred will divide without problem. The lower two digits cannot spoil the picture when they are transferred. I can go into more detail if you like.

As for simplicity, see above. Excel says mutually simple.

 

Oh, yes, divisibility by 4 is clear. Mutual simplicity you want to prove on a piece of paper.

You're good, though!

 
Mathemat >>:

Простоту хоцца доказать на бумажке.

Simplicity is proved by demonstrating indivisibility. Whether it's on a piece of paper or a calculator.

 
Mathemat >>:

Силен ты, однако!

I've got a little... :)))

Come on.

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