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Isomorphism's user avatar
Isomorphism's user avatar
Isomorphism
  • Member for 12 years, 6 months
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41 votes

Prove that odd perfect square is congruent to $1$ modulo $8$

9 votes
Accepted

How many ways are there to write $675$ as a difference of two squares?

8 votes

Prove that $\sum_{k=0}^{m}\frac{\binom{m}{k}}{\binom{n}{k}}=\frac{n+1}{n+1-m}$

8 votes

Let $p$ be an odd prime number. How many $p$-element subsets of $\{1,2,3,4, \ldots, 2p\}$ have sums divisible by $p$?

8 votes

Show that $f(x)$ has no repeated roots.

8 votes
Accepted

Is $10^n+1$ composite for all $n\in \mathbb{N}$ greater then $2$?

7 votes

Number of non decreasing sequences of length $M$

6 votes
Accepted

Evaluate the sum $ \sum_{i=0}^{n} (-1)^{n-i} \binom{n}{i} f(i)$

6 votes
Accepted

Induction of inequality involving AP

6 votes
Accepted

Solve $\sqrt[3]{x+10}-\sqrt[3]{x-10}=2$.

5 votes
Accepted

How to prove this inequality $x,y\in\Bbb R$, $|x|<1,|y|<1$ show that $\bigg|\frac{x-y}{1-xy}\bigg| < 1$ (and similar ones)

5 votes
Accepted

How to write in $2^x=5$ in logarithmic form?

4 votes

Solve the recurrence of $T(n)= 3T(n-1)+1$ with $T(0)=2$ by iteration of the recurrence

4 votes
Accepted

What is the best way to introduce for students the new mathematical definition : ‎$i^2=-1 ‎$?

4 votes
Accepted

$h\left(\frac{m}{2^n}\right)=0$ $\forall m\in\mathbb{Z},n\in\mathbb{N}$ implies $h(x)=0$ $\forall x\in\mathbb{R}$ if $h$ is continuous.

4 votes

How to prove $\sum^n_{k=0}\binom{n}k\cos\big((n-2k)\theta\big)=2^n\cos^n\theta$?

3 votes
Accepted

Using induction to prove P(k) with P(k-1)

3 votes
Accepted

Estimating $\pi$ very accurately

3 votes

How many ways are there to choose 10 objects from 6 distinct types when...

3 votes

How can I solve quadratic equations using modular arithmetic

3 votes
Accepted

Jordan Canonical form of a matrix over rationals whose all entries are 1.

3 votes
Accepted

Is $f:\mathbb Z \times \mathbb Z \to \mathbb Z$, $f(m,n)=31m+23n$ injective?

3 votes

Prove a group is abelian

3 votes

Theory and problems book in euclidean, affine, and projective geometry

2 votes
Accepted

Show that $f(z)=2z+z^2$ with $|z|<1$ is a one-to-one function

2 votes
Accepted

Proving $n^{17} \equiv n \;(\text{mod}\; 510)$

2 votes
Accepted

How many strings are there (inclusion exclusion principle)

2 votes
Accepted

A determinant from analytic geometry?

2 votes
Accepted

ABC a triangle with orthocenter and circumcenter at (9,5) and (0,0) respectively if equation of side BC is 2x-y=1 , then find possible coords of A?

2 votes

the highest common factor of $n-11$ and $3n+20$ is greater than 1?