# Proofs

Pro Problems > Math > Logic > Proofs# Featured Pro Problems

Prove that there is no two digit number which is the product of its digits

There are infinitely many angles between 0 and 90 degrees for which sine and cosine values are both rational. Create a proof.

Use a proof by induction to predict the value of the sum of the first n perfect squares.

Prove by contradiction that the harmonic mean of two positive numbers lies between the two numbers

Show that the trig identity given is true for all non-negative integers n.

Do a proof by induction to show what the sum of the first n positive integers is.

Show that the expression given is an irrational expression

Find, with proof, the digits place of a product of consecutive integers

# Full Directory Listing

Cubes and Nine, Ones Place Proof, Product of Digits, Rational Sine and Cosine, Squares Mod Four# Ask Professor Puzzler

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