Discrete Math
A Criterion for Divisibility by 3.
Prove that a number is divisible by 3 if the sum of its digits (when written in base 10) is divisible by 3. Again, it will help to remember what decimal notation means.
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Discrete Math A Criterion for Divisibility by 3. Prove that a number is divisible by 3...
Discrete Math: Divisibility (Need Help ASAP, will upvote) 1) Prove that if n is an odd positive integer, then n^2 is congruent to 1 (mod 8)
Divisibility by 9 To determine if a number is evenly divisible by 9, simply add all of the digits in that number. If the sum is divisible by 9, then the original number also is divisible by 9. For example, notice that all of the multiples of 9 from 1 through 12 (9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, and 108) contain digits which sum to 9 or 18 in every case. In another example, to...
11)Given below are two pais of statements .combine these two statements using if and only if (ii) p: If the sum of digits of a number is divisible by 3, then the number isdivisible by 3.q: If a number is divisible by3, then the sum of its digits is divisible by 3.
prove the product of 4 consecutive integers is always divisible by 24 using the principles of math induction. Could anyone help me on this one? Thanks in advance!Sure For induction we want to prove some statement P for all the integers. We need: P(1) to be true (or some base case) If P(k) => P(k+1) If the statement's truth for some integer k implies the truth for the next integer, then P is true for all the integers. Look at...
Exercise 7 (2 points) Recall the binomial coefficient for integer parameters 0 Sk< n. Prove that Exercise 8 (2 points) Prove the following: if z is an integer with at most three decimal digits aia2a3, then x is divisible by 3 if and only if aut a2 +a3 is divisible by 3. Exercise 9 (3 points) A square number is an integer that is the square of another integer. Let x and y be two integers, each of which can...
*these questions are related to Matlab The number 24 is exactly divisible by eight numbers (i.e. 1, 2, 3, 4, 6, 8, 12 and 24). The number 273 is also exactly divisible by eight numbers (i.e. 1, 3, 7, 13,21, 39, 91 and 273) There are 10 numbers in the range of 1:100 that are exactly divisible by eight numbers (i.e. 24, 30, 40, 42, 54, 56, 66, 70, 78 and 88). How many numbers in the range of n-1:20000...
will is playing a math game. He needs help to use the following clues to write a 5 digit number: 1.The number consists of 3 different digits 2.All digits are even numbers greater than zero 3.the value of the ones digit is one tenth of the value in the tens digit 4.The value of the tenths digit is 10 times as much as the value of the hundreds digit 5.The sum of the tenths and hundredths digits is equal to...
berry pie in town. What und you say! 6. Prove: If 3 divides the sum of the digits of a four digit decimal number, then 3 divides the number. DAD
Discrete Math 1: Please explain and prove each step with clear handwriting, and write every detail so that I can understand for future problems. This is discrete math one so please do not make it very complicated. PLEASE MAKE THE HANDWRITING AND THE STEPS CLEAR AND ORGANIZED Problem 2 (4 pts.): Solve the following recurrence relations together with the initial conditions. (a): an-2an-l + 3an-2 with ao = 2 and al = 4. (b): bn =-bn-l + 12bn-2 with bo...
Discrete Math: Please help with all parts of question 5. I have included problem 3 to help answer part (a) but I only need help with question 5! 5. 3. (a) (4 points) Prove that a graph is bipartite if and only if there is a 2-coloring (see problem 3) of its vertices. (b) (4 points) Prove that if a graph is a tree with at least two vertices, then there is a 2-coloring of its vertices. (Hint: Here are...