Proof : Every Integer Greater than 11 is the Sum of Two Composite Integers

Show that every integer greater than 11 is the sum of two composite integers.

Euclidean Algorithm : Finding the Greatest Common Divisor

Use the euclidean algorithm to find the greatest common divisor of 981 and 1234.

Proof : Prime Triplets

Show that there are no "prime triplets", that is numbers p, p+2, p+4, that are primes other than 3,5,7.

Consecutive Composite Integers

a) find the smallest 5 consecutive composite integers. b) find one million consecutive composite integers.

Real Analysis : Proof using Summation Integrals

For numbers a1,....,an, define p(x) = a1x +a2x^2+....+anx^n for all x. Suppose that: (a1)/2 + (a2)/3 +....+ (an)/(n+1) = 0 Prove that there is some point x in the interval (0,1) such that p(x) = 0