# Tagged Questions

Questions on congruences, linear diophantine equations, greatest common divisor, divisibility, etc.

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### Is 2 both a prime and a highly composite number?

I came across the definition of a highly composite number yesterday as a positive integer that has more divisors than any positive integer smaller than it. And, then I realised it would give 2 a very ...
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### Discriminant of a polynomial definition

Why is the discriminant of a polynomial defined as the product of squared differences of roots? How do I intuitively understand it? Why was this definition chosen?
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### How to factorize a number into prime numbers

I have to compute the Legendre symbol $4307 \choose 7549$, so I have to factorize $4307$ into prime numbers. Is there any mathematical shortcut to do it?
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### Prove that: $x^2+y^2+z^2=2xyz$ has no answer over $\Bbb{N}$

Prove that: $x^2+y^2+z^2=2xyz$ has no answer over $\Bbb{N}$ $$LHS=(x+y+z)^2-2(xy+yz+xz)=2xyz \implies (x+y+z)^2=2(xy+yz+xz)+2xyz$$ now what??
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### Weird Number patterns thinking process [closed]

The number pattern is -1 , 8 , -27 , 64 , -125 Find an expression for the nth term of the sequence . I'm been doing it by the guessing method for a few mins and couldn't get the answer . Can I get ...
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### Is it conjectured there infinitely primes $p$ such that M($p$) is a Mersenne Prime, where p is of an arithmetic progression?

Are there infinitely many primes $p$ of the form $an+d$ for fixed $a$ and $d$ coprime, and that $2^p-1$ is also prime? In other words, there are infinitely many primes $p$ $=$ $a$ $\pmod d$ ($a$ and ...
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### How to read a proof? [closed]

As I go deeper and deeper into upper division math courses, I find some proofs to be very challenging to understand. Right now I am trying to understand Gauss's lemma in number theory and I can't ...
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### Computing the Legendre symbol $6 \choose 11$

Compute the Legendre symbol $6 \choose 11$ By euler's critetion, ${6 \choose 11}=-1$, but ${6 \choose 11}={3 \choose 11 }{2\choose 11}=-1*-1=1$. I am confused about that result.
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### Is difference of two consecutive sums of consecutive integers (of the same length) always square?

I am an amateur who has been pondering the following question. If there is a name for this or more information about anyone who has postulated this before, I would be interested about reading up on it....