Theory of Numbers (VII) Principle of Mathematical Induction Fibonacci Number Suppose that F1 = 1, F2 = 1, F3 =1, F4 = 3, F5 = 5, and ...continues
Theory of Numbers (VIII) Principle of Mathematical Induction Fibonacci Number Pro ...continues
Theory of Numbers (IX) Principle of Mathematical Induction Fibonacci Number Prove that ...continues
Divisibility Rules for the numbers from 2 to 20
Derive rules to test whether a number is divisible by N, where N ranges from 2 to 20. E.g. A number is divisible by 3 if the sum of the digits is divisible by 3. Show that a palindromic number which has an even number of digits is always divisible by 11.
Can any set that is not a group (Z for example) still be a ring or is it necessary that a set must be a group to be a ring? Please give an example and counter example.
Theory of Numbers (X) Principle of Mathematical Induction Fibonacci Number Prove that (Fn+1)^2 – Fn Fn+2 = (- 1)^n ...continues
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 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 desc ...continues
