Question

Let $a = \frac{1 + \sqrt{2009}}{2}$ . Find the value of $(a^3 - 503a - 500)^5$ .

score 1k · Answer 1 · 2026-04-16 00:53:15

1k

Views

Let $a = \frac{1 + \sqrt{2009}}{2}$ . Find the value of $(a^3 - 503a - 500)^5$ .

Published on 16 Apr 2026 - 0:53

score 27 · Answer 2 · 2026-04-09 23:30:11

27

Views

A work problem on complex variable

Published on 09 Apr 2026 - 23:30

score 66 · Answer 3 · 2026-04-11 07:37:05

66

Views

solving existence problems in measure theory

Published on 11 Apr 2026 - 7:37

score 73 · Answer 4 · 2026-04-15 18:33:42

73

Views

how many integers $n$ have the property that there exist positive integers $a,b,c$ such that $a^n+b^ n=c^n$?

Published on 15 Apr 2026 - 18:33

score 38 · Answer 5 · 2026-04-13 04:44:37

38

Views

Solution of Differential equation by series

Published on 13 Apr 2026 - 4:44

score 382 · Answer 6 · 2026-04-14 20:29:48

382

Views

Given that $p$ is a prime, and the sum of all positive divisors of $p^4$ is a perfect square, find the possible number of primes $p$ .

Published on 14 Apr 2026 - 20:29

score 182 · Answer 7 · 2026-04-14 01:43:13

182

Views

Given a finite number of stones. We place every stone on an integer. Prove that, given different movements, we can only make finite number of moves

Published on 14 Apr 2026 - 1:43

score 233 · Answer 8 · 2026-04-13 23:52:37

233

Views

Normal distribution - What should be value of $x$ if the company wants no more than $0.5\%$ of the packets to be underweight?

Published on 13 Apr 2026 - 23:52

score 226 · Answer 9 · 2026-04-16 00:37:10

226

Views

Find the number of positive integers $n < 2007$ such that $\Big[\frac{n}{2}\Big]$ + $\Big[\frac{n}{3}\Big]$ + $\Big[\frac{n}{6}\Big] = n$ .

Published on 16 Apr 2026 - 0:37

score 219 · Answer 10 · 2026-04-16 14:34:37

219

Views

Find the number of real values of $x$ such that $x^2 + 10000[x] = 10000x$ ($[]$ is the floor function)

Published on 16 Apr 2026 - 14:34

score 108 · Answer 11 · 2026-04-16 04:49:10

108

Views

We have an integer n. We have n boxes where each box contains a non-negative amount of balls. Find all the permutations which satisfy some criteria

Published on 16 Apr 2026 - 4:49

score 322 · Answer 12 · 2026-04-14 23:29:41

322

Views

For which values of integer $k$, does the equation $x^2+y^2+z^2=kxyz$ have positive integer solutions $(x, y, z)$

Published on 14 Apr 2026 - 23:29

score 380 · Answer 13 · 2026-04-14 13:14:26

380

Views

Difference of induction and divide and conquer

Published on 14 Apr 2026 - 13:14

score 100 · Answer 14 · 2026-04-13 18:35:36

100

Views

Given a scalene triangle ABC and D, E, F the middle of BC, CA, AB respectively, prove that certain lines coincide

Published on 13 Apr 2026 - 18:35

score 55 · Answer 15 · 2026-04-11 09:59:37

55

Views

Conventions for defining inductive base case

Published on 11 Apr 2026 - 9:59

List Question

Let $a = \frac{1 + \sqrt{2009}}{2}$ . Find the value of $(a^3 - 503a - 500)^5$ .

A work problem on complex variable

solving existence problems in measure theory

how many integers $n$ have the property that there exist positive integers $a,b,c$ such that $a^n+b^ n=c^n$?

Solution of Differential equation by series

Given that $p$ is a prime, and the sum of all positive divisors of $p^4$ is a perfect square, find the possible number of primes $p$ .

Given a finite number of stones. We place every stone on an integer. Prove that, given different movements, we can only make finite number of moves

Normal distribution - What should be value of $x$ if the company wants no more than $0.5\%$ of the packets to be underweight?

Find the number of positive integers $n < 2007$ such that $\Big[\frac{n}{2}\Big]$ + $\Big[\frac{n}{3}\Big]$ + $\Big[\frac{n}{6}\Big] = n$ .

Find the number of real values of $x$ such that $x^2 + 10000[x] = 10000x$ ($[]$ is the floor function)

We have an integer n. We have n boxes where each box contains a non-negative amount of balls. Find all the permutations which satisfy some criteria

For which values of integer $k$, does the equation $x^2+y^2+z^2=kxyz$ have positive integer solutions $(x, y, z)$

Difference of induction and divide and conquer

Given a scalene triangle ABC and D, E, F the middle of BC, CA, AB respectively, prove that certain lines coincide

Conventions for defining inductive base case

Trending Questions

Popular # Hahtags

Popular Questions