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If a and b are odd integers, then 8|(a^2-b^2)

If a is an odd integer, then 24|a(a^2-1)

If a is an arbitrary integer, then 6|a(a^2+11)

Simple Absolute Value Problem

If a|b and b|c, with gcd(a,b)=1, then ab|c.

If gcd(a,b)=1, then gcd(a^2,b^2)=1.

If gcd(a,b)=1, d|ac, and d|bc, then d|c.

If gcd(a,b)=1 and c|(a+b), then gcd(a,c)=gcd(b,c)=1

Prove a property of a Parabola

Prove that the graph of the equation is a Hyperbola.

Prove that the graph of the equation is an Ellipse.

Slope and Equations of Lines

If gcd(a,b)=1, then gcd(ac,b)=gcd(c,b)

If gcd(a,b)=1 and c|a, then gcd(b,c)=1

If gcd(a,b)=1 and gcd(a,c)=1, then gcd(a,bc)=1.

Probability (Definition)

Complement and Mutually Exclusive Events

Sample Space and Events

Prove the Remainder Theorem for Polynomials

An Example of how the Division Algorith for Polynomials Works

Divide 18x^4+9x^3+3x^2 by 3x^2+1 using Long Division.

(ab)^-1=a^-1b^-1

(secx-cscx)/(secx+cscx)=(tanx-1)/(tanx+1)

Adding Fractions Proof