Introduction Keyword Cipher is another method of encrypting alphabetic text. It is a type of monoalphabetic substitution cipher. Monoalphabetic means an alphabet in plain text is mapped to one alphabet in the ciphertext. For example, if the plain text contains multiple occurrences of ‘A’ then all occurrences of ‘A’ are substituted by the same alphabet …
Given is not divisible by 5 Proof We will prove that the given statement is true by contradiction. Let . Assume is divisible by 5. Let, where The above equation is a quadratic equation. The roots of a quadratic equation are given by We know that . If then must also . This means that …
Introduction Vigenere Cipher is a method of encrypting alphabetic text. It is a polyalphabetic substitution cipher. Polyalphabetic substitution means that an alphabet in plain text is mapped to multiple substitution alphabets. Vigenere cipher is an evolution of Caesar cipher. In Caesar cipher, we shift the alphabets of the plain text by a fixed number of …
Given n(n+1)(2n+1) is divisible by 6 ∀ n ∈ N Proof STEP 1 : We will check if the statement is true for n = 1 n*(n + 1)*(2n + 1) = 1 * (1 + 1) * ( 2*1 + 1 ) = 1 * 2 * 3 = 6 The statement is true …
Prove by mathematical induction n(n+1)(2n+1) is divisible by 6 Read More »
Given If n is not divisible by 3 then n2-1 is divisible by 3 ∀ n ∈ Z Proof For the value of n, we have 3 choices Case 1 : n % 3 = 1 Let, P = (n2-1) % 3 P = ( ( n2 ) % 3 – 1 % 3 ) …
Prove that if n is not divisible by 3 then n^2-1 is divisible by 3 Read More »
Given 2n2 + n + 1 is not divisible by 3 ∀ n ∈ Z Proof We will prove the given statement by direct method. For each value n, we have three choices CASE 1 : n % 3 = 0 S = 2n2 + n + 1 Taking MOD 3 on both sides S …
Prove that if n is an integer then 2n^2+n+1 is not divisible by 3 Read More »
Given If 3n + 2 is odd then n is odd ∀ n ∈ Z Proof By Contradiction We will prove the given statement by contradiction Suppose 3n+2 is odd. Assume n is even. If n is even, then we can write n as n = 2k, k ∈ Z Substitute n in 3n+2 3(2k) …
Prove that if n is an integer and 3n + 2 is odd then n is odd Read More »
Given If 3n + 2 is even then n is even ∀ n ∈ Z Proof By Contradiction We will prove the given statement by contradiction Suppose 3n+2 is even. Assume n is odd. If n is odd, then we can write n as n = 2k + 1, k ∈ Z Substitute n in …
Prove that if n is an integer and 3n+2 is even then n is even Read More »
Given 1 + 3 + 5 + 7 + ⋯ + (2n-1) = n2 ∀ n ∈ N Proof We will prove the statement using mathematical induction. STEP 1 In this step, we check if the statement is true for n = 1. 1 + 3 + 5 + 7 + ⋯ + (2n-1) = …
Write a program to remove all zeros from a integer number in C/C++. For example, Input 809210003 Output 89213 Steps Take input from the user. Let it be N. Set num = 0. num will store the output. Repeat the following steps while N > 0 Set R = N % 10. This step stores …
