# Tag Info

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In short:
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### Can you find a 3x3 white square somewhere in this relatively prime graph?

One solution I've found Construction
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### Self-referential sequence that is sometimes powers of two

The sequence is defined as: For example, This explains the note that we the sequence can't start with two of the same number because To answer the questions: What comes after $115$ in the second ...
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### An Almost-squarish set of numbers

The first few almost-square numbers are: $3,8,15$ And we notice that $3\times 8=24$ is the next almost-square number. As such, we have the almost-squarish set $\{1,3,8\}$ with 3 distinct elements. If ...
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### Vector Sum of Pythagorean Triples

The graph of real-valued Pythagorean triples $x^2+y^2=z^2$ forms an infinite cone if we restrict to $z>0$: A sum of $n$ independent vectors on this cone is $n$ times their average, which lies ...

### How abundant can a number get?

Does such a number exist? We require a few priors: Where to begin?
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### Numbers whose product of digits is a multiple of sum of digits

Three numbers Observe that: Moreover: So we can start by finding... At this point it is worth noting that: So we search and find that Now observe that: So: With this much flexibility for ...

### An Almost-squarish set of numbers

The existence of a "Diophantine quintuple" was an open question for many years.

i) ii)

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### Intermingled primes

The 6 different primes are: Deductions (I solved it with regular expressions in a list of all prime numbers from 101-997):

### Primeable numbers

Let's try to understand the probability of very large unprimeable numbers. To do so, let's start by looking at how many permutations a number has. If a number has only a single unique digit, it has ...
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### Self-numbers and repunits

Are there infinitely many repunits which are not Self-numbers? Are there infinitely many Self-numbers which are repunits?
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### Same sequence interwoven with itself creating groups

It is Proof
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This may be a partial answer, because I don't see how to reverse the "encryption", and I'm not enough of a mathematician to confidently say this transform is not reversible. Explain how the ...
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### Smallest 3x3 Magic Square of different square sums

answer 1 (square sums) This is the smallest because... answer 2 (triangular sums) This is smallest because...

### Smallest Magic Hexagon Using Repeat Digits

My answer for the least sum along any line is