Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [contest-math]

For questions about mathematics competitions or the questions that typically appear in math competitions. Provide enough information about the source to confirm the question doesn't come from a live contest.

This tag is intended for

  1. Questions from mathematics competitions.
  2. Inquiries about alternative proofs for problems that are from math contests.
  3. Questions that have been inspired by a contest problem, including practice problems.
  4. Questions requesting advice on competing in contests.

See this list of mathematics competitions to get an idea of the types of questions this tag is for.

Mathematics StackExchange has a policy on questions from current competitions. Questions from ongoing competitions will be locked and temporarily deleted until the end of the contest. It is a good idea to include information about a contest, such as a link to the contest webpage.

9758 questions
1
vote
3 answers

Algebra Difference in Roots Question.

Let D be the absolute value of the difference of the 2 roots of the equation 3x^2-10x-201=0. Find [D]. [x] denotes the greatest integer less than or equal to x. I came across this question in a Math Competition and I am not sure how to solve it…
snivysteel
  • 1,104
1
vote
2 answers

Let $n$ be a positive integer. Show that if $2^n -1$ is a prime number, then $n$ is a prime number.

Let $n$ be a positive integer. Show that if $2^n -1$ is a prime number, then $n$ is a prime number. This is how I started to tackle this question: Assume that instead of $n$ being a prime number, it is a composite number. Let $n=ab$ where a and b…
user2574069
  • 51
1
vote
2 answers

question from russian math olympiad

Let $f(x,y)=\frac{1}{2}(x+y-1)(x+y-2)$ be a function of two positive integers. Prove that for any positive integer $z$ there exists a single pair $x,y$ such that $f(x,y)=z$. Isn't this clearly wrong? E.g. for $z=5$, there can be no successive…
user144248
  • 432
1
vote
4 answers

A function $f$ has the property that $f(x+y)=f(x)+f(y)+3xy$. If $f(1)=2$, what is $f(8)$?

A function $f$ has the property that $f(x+y)=f(x)+f(y)+3xy$. If f(1)=2, what is f(8)? I would like to try to tackle this problem but I need somewhere to start as I really have no idea at all on how to start. At first I assumed that perhaps $f$ was a…
user2574069
  • 51
1
vote
1 answer

Explain the following part of the exercise...

I've been looking at this IMO 2006 contest exercise and found a thing I cannot understand: The exercise is: Now what I do not understand is , why ??? Can you explain me this? Thank you in advance!
wonderingdev
  • 1,761
1
vote
4 answers

Sets of integers in the form $a^2 + 4ab + b^2$

Let $A$ be the set of all integers of the form $ a^2 + 4ab + b^2$ where $a, b$ are integers if $x, y$ are in $A$, prove that $xy$ is in $A$ (I have tried opening everything, it gets nowhere) Show that $121$ is in $A$ Show that $11$ is not in…
Yang Lu
  • 67
1
vote
1 answer

Probability that one buys bread Exactly Three times in the next Five minutes

The problem states that a typical customer buys the bread $60\%$ of the time and fruit $50\%$ of the time on each visit. Also the probability that the customers buy both bread and fruit is $0.3$. Then, what is the probability that a typical customer…
Free Spirit
  • 53
1
vote
1 answer

Average Train Speed

I'm repeating this question since they don't seem to like it over there: https://stackoverflow.com/questions/21972403/average-train-speed This is the question I have: If a train is traveling at 50 mph for 30 miles and makes 3 stops 15 min apart what…
AMahdy
  • 11
1
vote
2 answers

A tricky question from the AMC test (American Mathematics competitions)

A man walks into a store with just enough money to buy exactly 30 balloons, he then he discovers the store has a buy 1 get, one 1/3 off, sale. (a rather ridiculous sale if I do say so myself) how many balloons can he get? I don't know for sure if…
Diamond Louis XIV
  • 189
1
vote
1 answer

How to calculate time in this condition?

A starts at 11:00AM and travels at a speed of 4km/hr. B starts at 1:00PM and travels at 1km/hr for the first 1hr and 2km/hr for the next hr and so on. At what time they will meet each other ? Note - Both A and B starts from same point and travel in…
Android developer
  • 235
1
vote
1 answer

Proving there exist no positive integers $m,n$ such that $ m/n +(n+1)/m = 4$

Prove that there exist no positive integers $m,n$ such that $$ \frac{m}{n} + \frac{n+1}{m} = 4.$$ I worked on cases considering $m$ and $n$ are even or odd, but I couldn't get anything.
maths lover
  • 3,344
1
vote
1 answer

Checking whether the number is composite

Prove that $5^{125}-1$/ ($5^{25} - 1$) is composite I have written $5^{125}-1$ as $(5^{25}-1)(5^{100}+5^{75}+5^{50}+5^{25}+1)$ but what should I do after this? Sorry about earlier mistake in question ,
user114544
  • 11
1
vote
2 answers

Contest Math Possible Triangles

In the xy-plane, how many triangles have each of their vertices at points (a,b) where a,b are integers satisfying 1 ≤ a ≤ 5 and 1≤b≤5? I got twenty-five, but something tells me this isn't right. I set up an inequality, square root of a squared plus…
user87611
1
vote
2 answers

Square root of decimal Places

I'm searching to find how to get the sqaure root of a number having decimal places. How to find the Square root of say $0.4$?
user100520
  • 11
1
vote
2 answers

Determine the least natural number $k$ such that $a(k)>1$

Let $a(n)$ be a sequence with $a(0)=1/2$ and $a(n+1)=a(n)+(a(n)^2)/2013$, $n$ natural number. Determine the least natural number $k$ such that $a(k)>1$. This problem is from Poland proposed to Romanian Masters of Mathematics. Can you give me some…
user85046
1 2 3
…
31 32