Question

Two numbers whose difference is a full square are called friendly numbers. For example,....

score 96 · Answer 1 · 2026-04-12 22:26:27

96

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Two numbers whose difference is a full square are called friendly numbers. For example,....

Published on 12 Apr 2026 - 22:26

score 907 · Answer 2 · 2026-04-17 10:00:10

907

Views

Find the number of positive integers $n$ such that $\big(n + 2n^2 + 3n^3 + ... + 2005n^{2005}\big)$ is divisible by $(n-1)$.

Published on 17 Apr 2026 - 10:00

score 65 · Answer 3 · 2026-04-12 01:10:59

65

Views

Limit of sin function

Published on 12 Apr 2026 - 1:10

score 573 · Answer 4 · 2026-04-13 00:29:27

573

Views

Calculating the number of integers divisible by 8

Published on 13 Apr 2026 - 0:29

score 332 · Answer 5 · 2026-04-15 04:23:44

332

Views

If the total number of $3$-element subsets of $(1,$ ... $, 23)$ with $S(A) < 36$ is $N$. Find $\frac{(N+ 45)}{25}$.

Published on 15 Apr 2026 - 4:23

score 67 · Answer 6 · 2026-04-10 08:44:40

67

Views

Proof using the fixed point theorem

Published on 10 Apr 2026 - 8:44

score 726 · Answer 7 · 2026-04-12 10:14:20

726

Views

The difference between the HCF and LCM of $x$ and $18$ is $120$. Find $x$.

Published on 12 Apr 2026 - 10:14

score 646 · Answer 8 · 2026-04-12 22:30:14

646

Views

Find the highest natural number which is divisible by $30$ and has exactly $30$ different positive divisors.

Published on 12 Apr 2026 - 22:30

score 156 · Answer 9 · 2026-04-14 18:59:16

156

Views

Solving Equation of form: num = $x^3 + ax^2 + bx + c$.

Published on 14 Apr 2026 - 18:59

score 118 · Answer 10 · 2026-04-15 13:29:50

118

Views

Point $D$ is on line $BO$ such that $O$ is between $B$ and $D$ and $\angle ADC = \angle ABC$.

Published on 15 Apr 2026 - 13:29

score 74 · Answer 11 · 2026-04-14 10:11:38

74

Views

Given an acute triangle in a circle, prove the concyclicity of some points

Published on 14 Apr 2026 - 10:11

score 219 · Answer 12 · 2026-04-16 08:26:10

219

Views

A square appears randomly within a square of ten time its area. What is probability that the smaller square contains the larger square's center?

Published on 16 Apr 2026 - 8:26

score 80 · Answer 13 · 2026-04-17 18:04:52

80

Views

Find the sum of all the digits of the least positive integer $n$ such that $(P_2 * P_3 * $ ... $ * P_n)$ exceeds $2010$ .

Published on 17 Apr 2026 - 18:04

score 95 · Answer 14 · 2026-04-16 15:54:18

95

Views

If $\lfloor a-b\rfloor =2$, $\lfloor b-c\rfloor =3$, $\lfloor c-d\rfloor =4$, what is the sum of all possible values of $\lfloor a - d\rfloor?$

Published on 16 Apr 2026 - 15:54

score 398 · Answer 15 · 2026-04-08 19:59:23

398

Views

How to solve this tetration equation analytically?

Published on 08 Apr 2026 - 19:59

List Question

Two numbers whose difference is a full square are called friendly numbers. For example,....

Find the number of positive integers $n$ such that $\big(n + 2n^2 + 3n^3 + ... + 2005n^{2005}\big)$ is divisible by $(n-1)$.

Limit of sin function

Calculating the number of integers divisible by 8

If the total number of $3$-element subsets of $(1,$ ... $, 23)$ with $S(A) < 36$ is $N$. Find $\frac{(N+ 45)}{25}$.

Proof using the fixed point theorem

The difference between the HCF and LCM of $x$ and $18$ is $120$. Find $x$.

Find the highest natural number which is divisible by $30$ and has exactly $30$ different positive divisors.

Solving Equation of form: num = $x^3 + ax^2 + bx + c$.

Point $D$ is on line $BO$ such that $O$ is between $B$ and $D$ and $\angle ADC = \angle ABC$.

Given an acute triangle in a circle, prove the concyclicity of some points

A square appears randomly within a square of ten time its area. What is probability that the smaller square contains the larger square's center?

Find the sum of all the digits of the least positive integer $n$ such that $(P_2 * P_3 * $ ... $ * P_n)$ exceeds $2010$ .

If $\lfloor a-b\rfloor =2$, $\lfloor b-c\rfloor =3$, $\lfloor c-d\rfloor =4$, what is the sum of all possible values of $\lfloor a - d\rfloor?$

How to solve this tetration equation analytically?

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