Find Divisibility Rules for the Numbers from 2 to 13
Derive rules to test whether a number is divisible by N, where N ranges from 2 to 13. 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 : Fibonacci Numbers
Prove that (Fn+1)^2 – Fn Fn+2 = (- 1)^n
Theory of Numbers : Fibonacci Numbers
Principle of Mathematical Induction, Fibonacci Number Prove that F1F2 + F2F3 + F3F4 + …+ F2n – 1F2n = (F2n)^2.
Theory of Numbers : Fibonacci Numbers
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
Prove by contradiction that there does not exist a largest integer.
Prove by contradiction that there does not exist a largest integer. Hint: observe that for any integer n there is a greater one, say n+1. So begin the proof "Suppose for contradiction that there is a largest integer. Let this integer be n...."
Prove that y^2= x^3+23 has NO integer solutions.
1- prove : 1/2^2 + 1/3^2 +1/4^2+ ..... + 1/n^2 < 1
