User Noble Mushtak

73 votes

Accepted

Why is $A^TA$ invertible if $A$ has independent columns?

answered Jun 26, 2016 at 23:53

57 votes

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How to prove that a very large number is not prime

answered May 5, 2016 at 19:49

33 votes

Exactly when and why can a Turing-machine not solve the halting problem?

answered Dec 26, 2018 at 22:49

21 votes

Solving an equation, need help with explaining why one solution cant be true

answered Jun 29, 2016 at 21:56

15 votes

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I don't understand this definition of the integers.

answered May 25, 2016 at 23:46

12 votes

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Negation of "and" statements: a and b

answered Oct 23, 2016 at 1:12

10 votes

Minimize the function $f(y_1,y_2)=3 y_1^2+8y_2^2$

answered Jun 20, 2016 at 2:41

10 votes

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Proof of $+0 = -0$

answered Jan 31, 2016 at 14:47

9 votes

Accepted

Series $e^1+e^2+\:...\:+e^n$

answered Dec 25, 2016 at 15:09

9 votes

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Trying to parse a Putnam solution from 1995

answered Dec 30, 2018 at 0:52

9 votes

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Analytic continuation of harmonic series

answered Jan 1, 2019 at 14:00

8 votes

Accepted

The sequence defined by $x_{n}=\frac{x_{n-1}+x_{n-2}}{2}.$

answered Jun 24, 2016 at 15:46

8 votes

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Let $f$ be continuous on $[0,1]$ such that $\int_0^x f = \int_x^1 f$, what is $f$?

answered Dec 1, 2018 at 1:23

8 votes

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What is the relationship between the orbit-stabilizer theorem and Lagrange's theorem?

answered Dec 30, 2018 at 15:18

8 votes

If irrational numbers are uncountable, then why did I find this?

answered Dec 31, 2018 at 3:52

8 votes

Is there a way to find this limit algebraically? $\lim\limits_{x\to \infty} \frac{x}{\sqrt{x^2 + 1}}$

answered Jan 5, 2019 at 18:46

7 votes

What is the sum of the $81$ products in the $9 \times 9$ multiplication grid?

answered Jun 11, 2016 at 22:36

7 votes

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Any digit written $6k$ times forms a number divisible by $13$

answered May 8, 2016 at 11:30

7 votes

If every intermediate ring of a field extension is a field, then the extension is algebraic

answered May 15, 2016 at 11:32

7 votes

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Choosing code using digits and letters

answered Mar 26, 2016 at 18:46

7 votes

How do you create an alternating series with the sign being the same twice in a row?

answered Apr 16, 2016 at 21:01

7 votes

Accepted

Prove this using counting techniques: $\sum_{k=0}^{n}{\binom{2n+1}k} = 2^{2n}$

answered Jun 23, 2016 at 15:59

7 votes

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Are these two statements true or false?

answered Dec 25, 2016 at 13:28

7 votes

the New Year will be 2017: how many pairs of integer solutions to $x^2 + y^2 = (2017)^3$?

answered Dec 28, 2016 at 0:22

7 votes

Accepted

Stuck with this limit of a sum: $\lim _{n \to \infty} \left(\frac{a^{n}-b^{n}}{a^{n}+b^{n}}\right)$.

answered Dec 29, 2016 at 1:15

7 votes

If derivative goes to $0$, does the function have a limit?

answered Dec 28, 2018 at 22:59

6 votes

Accepted

Confusion about elements in fields, like -1 in Z5

answered Apr 22, 2016 at 18:51

6 votes

Accepted

Solve $(x+1)dx+e^ydy=0$ at (x,y)=(0,1)

answered Jun 12, 2016 at 23:40

6 votes

Accepted

What is the smallest possible value of $n$?

answered Jun 11, 2016 at 17:25

6 votes

Accepted

What are the kernels of ring homomorphisms that contain the polynomial $X^2+1$?

answered Mar 27, 2016 at 14:44

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580 Answers

Why is $A^TA$ invertible if $A$ has independent columns?

How to prove that a very large number is not prime

Exactly when and why can a Turing-machine not solve the halting problem?

Solving an equation, need help with explaining why one solution cant be true

I don't understand this definition of the integers.

Negation of "and" statements: a and b

Minimize the function $f(y_1,y_2)=3 y_1^2+8y_2^2$

Proof of $+0 = -0$

Series $e^1+e^2+\:...\:+e^n$

Trying to parse a Putnam solution from 1995

Analytic continuation of harmonic series

The sequence defined by $x_{n}=\frac{x_{n-1}+x_{n-2}}{2}.$

Let $f$ be continuous on $[0,1]$ such that $\int_0^x f = \int_x^1 f$, what is $f$?

What is the relationship between the orbit-stabilizer theorem and Lagrange's theorem?

If irrational numbers are uncountable, then why did I find this?

Is there a way to find this limit algebraically? $\lim\limits_{x\to \infty} \frac{x}{\sqrt{x^2 + 1}}$

What is the sum of the $81$ products in the $9 \times 9$ multiplication grid?

Any digit written $6k$ times forms a number divisible by $13$

If every intermediate ring of a field extension is a field, then the extension is algebraic

Choosing code using digits and letters

How do you create an alternating series with the sign being the same twice in a row?

Prove this using counting techniques: $\sum_{k=0}^{n}{\binom{2n+1}k} = 2^{2n}$

Are these two statements true or false?

the New Year will be 2017: how many pairs of integer solutions to $x^2 + y^2 = (2017)^3$?

Stuck with this limit of a sum: $\lim _{n \to \infty} \left(\frac{a^{n}-b^{n}}{a^{n}+b^{n}}\right)$.

If derivative goes to $0$, does the function have a limit?

Confusion about elements in fields, like -1 in Z5

Solve $(x+1)dx+e^ydy=0$ at (x,y)=(0,1)

What is the smallest possible value of $n$?

What are the kernels of ring homomorphisms that contain the polynomial $X^2+1$?