24 May 12, 09:23AM
(This post was last modified: 24 May 12, 04:41PM by Roflcopter.)
As requested by RCJD, here's a problems thread for everyone to contribute to. When you post a new question in the thread give it a number so we can keep track of them or this will get chaotic.
#1 (easy): Prove there are no Pythagorean triplets (a, b, c) such that a b and c are all primes.
#2 (easy): Prove by construction that Q is dense in R. That is, for any real numbers x and x' (with x < x') find a fraction a/b with x < a/b < x' (a and b are integers, b is non-zero).
#3 (medium, requires programming): Find the number of squarefree numbers less than![[Image: png.latex?10%5E%7B12%7D]](http://latex.codecogs.com/png.latex?10%5E%7B12%7D)
.
#4 (medium, requires programming): How many primes are there less than 123456789109?
#5 (medium): Find all solutions to![[Image: png.latex?x%5Ey=y%5Ex]](http://latex.codecogs.com/png.latex?x%5Ey=y%5Ex)
with x and y positive integers.
#1 (easy): Prove there are no Pythagorean triplets (a, b, c) such that a b and c are all primes.
#2 (easy): Prove by construction that Q is dense in R. That is, for any real numbers x and x' (with x < x') find a fraction a/b with x < a/b < x' (a and b are integers, b is non-zero).
#3 (medium, requires programming): Find the number of squarefree numbers less than
#4 (medium, requires programming): How many primes are there less than 123456789109?
#5 (medium): Find all solutions to