Theory of Numbers (X): Principle of Mathematical Induction: Fibonacci Number: Prove that (Fn+1)^2 – Fn Fn+2 = (- 1)^n

Theory of Numbers (X) Principle of Mathematical Induction Fibonacci Number Prove that (Fn+1)^2 – Fn Fn+2 = (- 1)^n

Theory of Numbers (XI): Principle of Mathematical Induction: Fibonacci Number: Prove that F1F2 + F2F3 + F3F4 + …+ F2n – 1F2n = (F2n)^2.

Theory of Numbers (XI) Principle of Mathematical Induction Fibonacci Number Prove that F1F2 + F2F3 + F3F4 + …+ F2n – 1F2n = (F2n)^2.

Theory of Numbers (XII): Principle of Mathematical Induction: Fibonacci Number: Prove that F1F2 + F2F3 + F3F4 + …+ F2n F2n+1 = (F2n+1)^2 - 1.

Theory of Numbers (XII) Principle of Mathematical Induction Fibonacci Number Prove that F1F2 + F2F3 + F3F4 + …+ F2n F2n+1 = (F2n+1)^2 – 1.

Theory of Numbers Fermat's Theorem Let p and q be prime number greater than 3. Prove that 24|p^2-q^2

Let p and q be prime number greater than 3. Prove that 24|p^2-q^2

Need to prove: If x is a real number and x^2=3, then x is irrational.

Need to prove: 1.) If x is a real number and x^2=3, then x is irrational. 2.) The proposition "if x is a real number and x^2=4, then x is irrational." is false since x=2=2/1 is rational and 2^2=4. Pinpoint where in the previous argument the proof of this proposition breaks down. See attached file for full problem description.