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ibhar

5 Questions
4 Answers

0

330

3

+31

Really fun conditions problem

Find all integers such that the arithmetic mean of all its factors is an integer.

Thanks so much!

ibhar Mar 13, 2022

+1

363

2

+31

Proof - distribution of primes!

Hello!

Prove that for all , the number of primes from to inclusive, is greater than .
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ibhar Mar 13, 2022

+1

411

4

+31

Proof with simple rational function

Prove that for all positive integers
is never a perfect square.

This seems so simple but I don't see any efficient way of starting on this problem... read more ..

ibhar Mar 12, 2022

0

395

2

+31

Beautiful intricate math problem

Hello! Here is a really fun problem I came up with.

You are given a perfect square
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ibhar Jan 22, 2022

+1

443

2

+31

Strange property of fibbinary numbers - proof

A fibbinary number is a number whose binary representation contains no consecutive s.

Prove that the number of non-negative fibbinary numbers less than or equal to is always .
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ibhar Jan 15, 2022

+31

+1

Oh! That's really cool! I haven't thought of the odd primes.

I also assume that some non-odd primes work and as you say, some even numbers work too. Is there a specific way of describing them or is it just at random?

Thank you so much,geno3141!

ibharMar 14, 2022

+31

-1

More info:

I tried different values of $x$ up to $10^8$ with a program and never was $\frac{x^5-1}{x-1}$ a perfect square...

Can you find a proof?

thx

ibharMar 13, 2022

+31

-1

Now, can you prove that $x=3$ is the ONLY value of $x$ for which $\frac{x^5-1}{x-1}$ is a perfect square??

Tysm.

ibharMar 12, 2022

+31

-1

What is your solution to this problem? I'm curious.

ibharJan 23, 2022