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42 votes
8 answers
21k views

Why $\gcd(b,qb+r)=\gcd(b,r),\,$ so $\,\gcd(b,a) = \gcd(b,a\bmod b)$

15 votes
2 answers
36k views

Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]

10 votes
2 answers
7k views

How to prove that $z\gcd(a,b)=\gcd(za,zb)$

9 votes
6 answers
10k views

Proof $f(\emptyset)=\emptyset$

8 votes
2 answers
4k views

$K_6$ contains at least two monochromatic $K_3$ graphs.

6 votes
1 answer
3k views

Proving formulas for $\cos(nx)$ and $\sin(nx)$

4 votes
2 answers
256 views

Proof of $f(\{x\})=\{f(x)\}$

4 votes
1 answer
752 views

Limit of quotient is zero if denominator goes to infinity and numerator is bounded

4 votes
1 answer
2k views

Limit of sum of unbounded and bounded sequence

3 votes
1 answer
3k views

Integral of $x^\alpha$ for Various $\alpha$

3 votes
2 answers
136 views

Eleven test on integers

3 votes
1 answer
5k views

Hindu calendar (lunar) to Gregorian calendar

2 votes
2 answers
1k views

Matrix column and row space basis

2 votes
2 answers
360 views

Invertible elements of $\mathbb Z/pq\mathbb Z$

2 votes
1 answer
190 views

If $f$ is at least degree $1$, then $f(n)$ cannot be prime for all n

2 votes
4 answers
134 views

Construct $\frac{1}{z}$ from $z \in \mathbb{C}$

2 votes
2 answers
96 views

Probabilistic question

2 votes
2 answers
193 views

Vector space base and dimension

2 votes
1 answer
222 views

Geometric interpretation

2 votes
1 answer
87 views

Something about limits

1 vote
4 answers
260 views

Inverse triangle equality [duplicate]

1 vote
4 answers
235 views

Diverging sequence

1 vote
1 answer
2k views

Proof that a sequence is divergent

1 vote
2 answers
135 views

Limit of powers

1 vote
2 answers
388 views

Any converging sequence is bounded

1 vote
3 answers
3k views

When is $f(x)=x^2-2x$ injective?

1 vote
1 answer
51 views

What are the elements according to the statement?

1 vote
1 answer
144 views

Proving $\bigcup_{n=1}^{\infty}\bigcap_{k=n}^{\infty}A_k \subseteq \bigcap_{n=1}^{\infty}\bigcup_{k=n}^{\infty}A_k$, and a condition for equality

1 vote
3 answers
312 views

Choice of $\xi$ [duplicate]

1 vote
1 answer
306 views

Draw $\frac{1}{z}$ in the complex plane