User questionasker

8 votes

2 answers

183 views

Nested functions

functions

asked Aug 12, 2020 at 14:25

5 votes

2 answers

130 views

Finding $\frac{2a^5 - 5a^4 + 2a^3 - 8a^2}{a^2 + 1}$

polynomials roots

asked Sep 16, 2020 at 3:03

4 votes

2 answers

88 views

Finding the length of $DE$ given $AB = 4$ and $BE = 5$

geometry power-of-the-point

asked Dec 19, 2020 at 4:24

3 votes

2 answers

70 views

Finding $\frac{DK}{DI}$

geometry

asked Feb 14, 2021 at 21:30

3 votes

2 answers

61 views

Finding the amount of prime numbers in $S_1, S_2,S_3,\ldots$

sequences-and-series

asked Nov 29, 2020 at 3:57

3 votes

4 answers

296 views

Arithmetic progression $(a,b,c)$ with $a^2+b^2=c^2$ and $\gcd(a,b,c) = 1$

elementary-number-theory arithmetic-progressions pythagorean-triples

asked Aug 12, 2020 at 13:43

3 votes

3 answers

62 views

Congruent sets of an arithmetic sequence and a geometric sequence

elementary-set-theory proof-writing quadratics arithmetic-progressions geometric-progressions

asked Aug 16, 2020 at 16:34

3 votes

3 answers

81 views

Finding the greatest common divisor of $(n+1)(n+2)^2(n+3)^3(n+4)^4$

elementary-number-theory

asked Feb 18 at 21:15

2 votes

2 answers

28 views

Finding the sum of $5$ angles given equivalent division of a side

analytic-geometry

asked Feb 22 at 22:27

2 votes

1 answer

80 views

Proving that there exists $\leq 1$ pairs in the sequence $a_{n+1} = a_n + \frac{n}{a_n}$ whose sum is a positive integer

elementary-number-theory

asked Feb 24 at 2:28

2 votes

2 answers

162 views

Recursive sequence with square roots

recursion

asked Aug 10, 2020 at 2:34

2 votes

3 answers

100 views

Solving for $x$ when $\sqrt{\sqrt{3} - \sqrt{\sqrt{3} + x}} = x$

algebra-precalculus

asked Sep 17, 2020 at 15:32

2 votes

3 answers

65 views

Finding $x$ when $\sqrt{3x - 4} + \sqrt[3]{5 - 3x} = 1$

radicals

asked Sep 17, 2020 at 20:18

2 votes

2 answers

93 views

Integer roots to $ax^2 + bx + c$ and $(a+1)x^2 + (b+1)x + (c+1)$

roots quadratics

asked Sep 24, 2020 at 17:10

2 votes

0 answers

25 views

Finding a relationship between $a,b,c$ when given that $x^2 - ax - y + b^2 + ac = 0$

solution-verification triangles

asked Sep 28, 2020 at 18:41

2 votes

2 answers

62 views

Finding all possible values of $d$ given that the sum of the reciprocals of a polynomial is $17$

sequences-and-series polynomials roots geometric-progressions

asked Oct 1, 2020 at 19:57

2 votes

2 answers

110 views

Finding $k$ such that $x^2 + x + 10 = k(k-1)$ has one positive integer root

discriminant

asked Oct 19, 2020 at 17:10

2 votes

2 answers

99 views

Finding $m$ given that $9m^2 + 25m + 26$ is a product of consecutive integers

discriminant

asked Oct 23, 2020 at 17:09

2 votes

1 answer

73 views

Finding $1998x + 5y + 3z$ given $\frac{1}{x} + \frac{1}{y} = \frac{3}{z}$

diophantine-equations

asked Oct 31, 2020 at 14:17

2 votes

1 answer

60 views

Proving that $\angle AOE = 2 \angle COD$ using complex numbers

geometry complex-numbers

asked Feb 6, 2021 at 18:00

2 votes

1 answer

146 views

Finding the number of $2017$-digit numbers with leading digit $2$

combinatorics

asked Feb 28, 2021 at 18:18

1 vote

3 answers

107 views

Finding all rational values of $x$ for which $256(x + 15\{x\})\{x\} = 2021$

fractional-part

asked Mar 17, 2021 at 19:31

1 vote

1 answer

66 views

Finding the least number of plants watered by three gardeners

combinatorics discrete-mathematics inclusion-exclusion

asked Jan 29, 2021 at 20:52

1 vote

1 answer

56 views

Finding $\sum_{n=2}^8 \frac{1}{n!(17-n)!}$

factorial

asked Feb 26, 2021 at 23:31

1 vote

1 answer

91 views

Finding $\sqrt{\frac{y}{x}} + \sqrt{\frac{z}{y}} + \sqrt{\frac{x}{z}}$

systems-of-equations

asked Mar 26, 2021 at 20:24

1 vote

2 answers

97 views

Finding $\frac{S_{\triangle BKC}}{S_{\triangle ABC}}$

geometry

asked Feb 11, 2021 at 20:42

1 vote

1 answer

63 views

Numbers that can be expressed as $ab + a + b$

integers

asked Jan 16, 2021 at 21:30

1 vote

1 answer

68 views

Proving that $pr$ and $qs$ are perpendicular

geometry

asked Oct 23, 2020 at 0:38

1 vote

2 answers

66 views

Finding all integer solutions of $\frac{1}{x} + \frac{1}{y} - \frac{1}{z} = \frac12$

diophantine-equations

asked Oct 28, 2020 at 18:58

1 vote

1 answer

33 views

Finding $S_{ADE}:S_{DBCE}$ given that $\angle A = 30^\circ$

euclidean-geometry triangles circles area plane-geometry

asked Oct 15, 2020 at 15:55

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84 Questions

Nested functions

Finding $\frac{2a^5 - 5a^4 + 2a^3 - 8a^2}{a^2 + 1}$

Finding the length of $DE$ given $AB = 4$ and $BE = 5$

Finding $\frac{DK}{DI}$

Finding the amount of prime numbers in $S_1, S_2,S_3,\ldots$

Arithmetic progression $(a,b,c)$ with $a^2+b^2=c^2$ and $\gcd(a,b,c) = 1$

Congruent sets of an arithmetic sequence and a geometric sequence

Finding the greatest common divisor of $(n+1)(n+2)^2(n+3)^3(n+4)^4$

Finding the sum of $5$ angles given equivalent division of a side

Proving that there exists $\leq 1$ pairs in the sequence $a_{n+1} = a_n + \frac{n}{a_n}$ whose sum is a positive integer

Recursive sequence with square roots

Solving for $x$ when $\sqrt{\sqrt{3} - \sqrt{\sqrt{3} + x}} = x$

Finding $x$ when $\sqrt{3x - 4} + \sqrt[3]{5 - 3x} = 1$

Integer roots to $ax^2 + bx + c$ and $(a+1)x^2 + (b+1)x + (c+1)$

Finding a relationship between $a,b,c$ when given that $x^2 - ax - y + b^2 + ac = 0$

Finding all possible values of $d$ given that the sum of the reciprocals of a polynomial is $17$

Finding $k$ such that $x^2 + x + 10 = k(k-1)$ has one positive integer root

Finding $m$ given that $9m^2 + 25m + 26$ is a product of consecutive integers

Finding $1998x + 5y + 3z$ given $\frac{1}{x} + \frac{1}{y} = \frac{3}{z}$

Proving that $\angle AOE = 2 \angle COD$ using complex numbers

Finding the number of $2017$-digit numbers with leading digit $2$

Finding all rational values of $x$ for which $256(x + 15\{x\})\{x\} = 2021$

Finding the least number of plants watered by three gardeners

Finding $\sum_{n=2}^8 \frac{1}{n!(17-n)!}$

Finding $\sqrt{\frac{y}{x}} + \sqrt{\frac{z}{y}} + \sqrt{\frac{x}{z}}$

Finding $\frac{S_{\triangle BKC}}{S_{\triangle ABC}}$

Numbers that can be expressed as $ab + a + b$

Proving that $pr$ and $qs$ are perpendicular

Finding all integer solutions of $\frac{1}{x} + \frac{1}{y} - \frac{1}{z} = \frac12$

Finding $S_{ADE}:S_{DBCE}$ given that $\angle A = 30^\circ$