MH1812
Discrete Mathematics
Contents
Prove that 2 is irrational.\text{Prove that } \sqrt{2} \text{ is irrational.}
If x and y are integers such that 5∤xy, then 5∤x and 5∤y.\text{If }x \text{ and } y \text{ are integers such that } 5 \nmid xy, \text{ then } 5 \nmid x \text{ and } 5 \nmid y.
Prove that for any positive integer n,1⋅2+2⋅3+…+n(n+1)=n(n+1)(n+2)3\text{Prove that for any positive integer } n, 1\cdot2 + 2\cdot 3 + \ldots + n(n+1) = \frac{n(n+1)(n+2)}{3}
Show that if n is an integer ≥1,then n can be written as a product of primes.\text{Show that if }n \text{ is an integer } \ge 1, \text{then } n \text{ can be written as a product of primes.}
