Games
Problems
Go Pro!

Infinite Primes

Pro Problems > Math > Logic > Proofs > Indirect Proofs
 

Infinite Primes

Use an indirect proof to show that there are infinitely many prime numbers.

Presentation mode
Problem by Mr. Twitchell

Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
Assign this problem
Click here to assign this problem to your students.

Similar Problems

Harmonic Proof

Create an indirect proof for the following statement: The harmonic mean of any two positive numbers lies inclusively between the two numbers.

A Smaller Fraction

For every positive rational number x, there exists a smaller positive rational number y. Prove this statement by indirect proof.

Radical Two Proof

Prove that
2
is an irrational number using an indirect proof, or proof by contradiction.

Hint: An irrational number is a number which cannot be written as the quotient of two relatively prime integers.

X Squared Proof

Prove by indirect method that if x and y are integers, then x2 - 9y ≠ 3.

X, Y, and Z proof

Prove by contradiction: for any integers x, y, and z with z > 1, x2 - yz2 ≠ z.

Hint: This is a more generalized version of the problem found here: X Squared Proof

Irrational Fraction

Let a and b be positive integers, with b not a perfect square. Show that the following expression is irrational, using an indirect proof.

a +
b
a -
b

Hint: Remember that an irrational number is a number which cannot be written as the quotient of two integers.

Sum of Trig Functions

Show that if θ is between 0º and 90º inclusive, then sin θ + cos θ ≥ 1. Use an indirect proof.

Ask Professor Puzzler

Do you have a question you would like to ask Professor Puzzler? Click here to ask your question!
Over 3,000 Pages of Free Content
We've been providing free educational games and resources since 2002.

Would you consider a donation of any size to help us continue providing great content for students of all ages?

Like us on Facebook to get updates about new resources
Home
Pro Membership
About
Privacy