Question

Let n ≥ 1 be an integer. Use the Pigeonhole Principle to prove that in any...

Let n ≥ 1 be an integer. Use the Pigeonhole Principle to prove that in any set of n + 1 integers from {1, 2, . . . , 2n}, there are two elements that are consecutive (i.e., differ by one).

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Using pigeonhole principle prove that in any group of 5 integers, not necessarily consecutive, there are...
Using pigeonhole principle prove that in any group of 5 integers, not necessarily consecutive, there are 2 with same remainder when divided by 9
Use Pigeonhole Principle to prove that there is some n ∈ N such that 101n −...
Use Pigeonhole Principle to prove that there is some n ∈ N such that 101n − 1 is divisible by 19. (Hint: Consider looking at numbers of the form 101k.)
Let n be a positive integer and let S be a subset of n+1 elements of...
Let n be a positive integer and let S be a subset of n+1 elements of the set {1,2,3,...,2n}.Show that (a) There exist two elements of S that are relatively prime, and (b) There exist two elements of S, one of which divides the other.
Use the Strong Principle of Mathematical Induction to prove that for each integer n ≥28, there...
Use the Strong Principle of Mathematical Induction to prove that for each integer n ≥28, there are nonnegative integers x and y such that n= 5x+ 8y
1. Prove that an integer a is divisible by 5 if and only if a2 is...
1. Prove that an integer a is divisible by 5 if and only if a2 is divisible by 5. 2. Deduce that 98765432 is not a perfect square. Hint: You can use any theorem/proposition or whatever was proved in class. 3. Prove that for all integers n,a,b and c, if n | (a−b) and n | (b−c) then n | (a−c). 4. Prove that for any two consecutive integers, n and n + 1 we have that gcd(n,n + 1)...
Let n be any integer, prove the following statement: n3+ 1 is even if and only...
Let n be any integer, prove the following statement: n3+ 1 is even if and only if n is odd.
3.a) Let n be an integer. Prove that if n is odd, then (n^2) is also...
3.a) Let n be an integer. Prove that if n is odd, then (n^2) is also odd. 3.b) Let x and y be integers. Prove that if x is even and y is divisible by 3, then the product xy is divisible by 6. 3.c) Let a and b be real numbers. Prove that if 0 < b < a, then (a^2) − ab > 0.
Use mathematical induction to prove that for each integer n ≥ 4, 5n ≥ 2 2n+1...
Use mathematical induction to prove that for each integer n ≥ 4, 5n ≥ 2 2n+1 + 100.
Prove, using induction, that any integer n ≥ 14 can be written as a sum of...
Prove, using induction, that any integer n ≥ 14 can be written as a sum of a non-negative integral multiple of 3 and a non-negative integral multiple of 8, i.e. for any n ≥ 14, there exist non-negative integers a and b such that n = 3a + 8b.
Prove let n be an integer. Then the following are equivalent. 1. n is an even...
Prove let n be an integer. Then the following are equivalent. 1. n is an even integer. 2.n=2a+2 for some integer a 3.n=2b-2 for some integer b 4.n=2c+144 for some integer c 5. n=2d+10 for some integer d
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT