Homework Statement
prove:6 divides (n^3-n) for all integers n.
Homework Equations
n^3-n=(n)(n+1)(n-1)
The Attempt at a Solution
tried to use direct proof. Then used cases that involed n=2k for some integer k and n=2k+1 for some integer k. However, i could not get it so that 6 was...
[SOLVED] basic math proof by contradiction
Homework Statement
prove: If a and b are positive numbers, a/b +b/a>=2
Homework Equations
The Attempt at a Solution
by contradiction (a^2+b^2)/ab<2 and got lost