Lambert macuse's user avatar
Lambert macuse's user avatar
Lambert macuse's user avatar
Lambert macuse
  • Member for 4 years, 10 months
  • Last seen more than a month ago
16 votes
1 answer
514 views

Children's Fruit Division

13 votes
3 answers
1k views

Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $

11 votes
0 answers
466 views

Simplify: $\frac{\sqrt{10+\sqrt{1}}+\sqrt{10+\sqrt{2}}+\ldots+\sqrt{10+\sqrt{99}}}{\sqrt{10-\sqrt{1}}+\sqrt{10-\sqrt{2}}+\ldots+\sqrt{10-\sqrt{99}}}$ [duplicate]

8 votes
0 answers
235 views

A triangle's sides are integers, and its circumradius is a prime number. Prove that the triangle is right-angled.

8 votes
3 answers
858 views

What fraction is shaded?

7 votes
4 answers
476 views

Choosing at least 2 women from 7 men and 4 women

6 votes
1 answer
634 views

Paths in a square grid with diagonal moves allowed

6 votes
3 answers
244 views

Prove that $\angle ABC <$ $ 84^\circ$.

6 votes
4 answers
204 views

How many numbers have the form $10n+d$ where $d$ is a non-zero digit?

5 votes
2 answers
138 views

$n$ people at a party and friendship

5 votes
1 answer
170 views

Determine the smallest positive integer $ m $ for which $\underbrace{100^{100^{\ldots^{100}}}}_m>\underbrace{3^{3^{\ldots^3}}}_{100}$

5 votes
1 answer
97 views

The moab Problem

5 votes
0 answers
99 views

Are there polynomials $P, Q$ with degree no less than 2018 and with integer coefficients, such that $P(Q(x))=3Q(P(x))+1$ for all real $x$?

4 votes
1 answer
70 views

Bank's Board of Executive Officers

4 votes
5 answers
380 views

Solving $\sqrt{x+4}-2 =x$ for $x ≠ 0$.

4 votes
1 answer
62 views

Calculate the value of the expression for polynomial roots

4 votes
3 answers
135 views

Find the value of $x$ in the figure

4 votes
1 answer
868 views

For $z=f(x,y)$ with $(x,y)=(r\cos\theta,r\sin\theta)$, show that $z_{xx}+z_{yy}=z_{rr}+ \frac{1}{r^2}z_{\theta \theta} + \frac{1}{r} z_r$

4 votes
4 answers
215 views

Calculate the number of solutions

4 votes
2 answers
1k views

Demonstrate that there are no perfect squares ending with $8$ [duplicate]

4 votes
0 answers
66 views

Euclidean division $n$ and $m$

4 votes
1 answer
141 views

What is the strategy to always win?

3 votes
1 answer
54 views

A particle falls from a height h of a ramp

3 votes
1 answer
86 views

Intersection of circles lie on an angle bisector

3 votes
0 answers
52 views

Game with number theory

3 votes
4 answers
170 views

Following Fibonacci

3 votes
1 answer
145 views

X lies on Polar of T.

3 votes
1 answer
152 views

Arbitrarily small lengths of segments inside convex polygon

3 votes
3 answers
214 views

Fixed points of the arithmetic derivative

3 votes
0 answers
88 views

Determine All Functions $f:[0,1] \to \mathbb{R}$

1
2 3 4 5
10