se one) is an integer and x<4 is an integer and x>1} is an integer and x21} is an integer and l

Q: Prove that Va - Vb is irrational number if 'a' and 'b’ are prime number?

A: Given To prove that a-b is irrational number if a and b are prime number.

Q: Use a direct proof to show that the sum of two odd integers is even.

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Q: write down the proof of the statement " √2 + √5 is not rational" in latex

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Q: what

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Q: Determine the number of natural numbers less than 700 that can be written using the digtits 5,6,7,9?

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Q: Two distinct numbers are selected from the set (1,2,3,4,...,36,37) so that the sum of the remaining…

A: Given two distinct numbers are selected from the set 1,2,3,4,…,36,37 and The sum of remaining 35…

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Q: How many pairs of two distinct integers chosen from the set {1, 2, 3,..., 101} have a sum that is…

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Q: Prove that for any 9 consecutive natural numbers, there exists one number that is prime to the other…

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Q: How many positive integers less than 1000 (1) are divisible by 7? (2) are divisible by 7 but not by…

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Q: Show that √17 is Irrational number

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A: Given: "Every positive integer can be written as the sum of the square of 3 positive integers." To…

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Q: fermat's theorm states, if p is prime & a is a positive integer not divisible by p then-------- and…

A: Fermat's Theorem: If p is a prime and a is a positive integer and not divisible by the prime p, then…

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A: Fermat number.

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Q: Prove disprove that or characteristics of simple xing is either prime . žero or

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Q: How many pairs of two distinct integers chosen from the set {1, 2, 3, 101} have a sum that is even?

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Q: If a and b are integers with gcd(a, b) =d Then gea (-) -- gcd

A: False

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A: Given that c divides a and b ,d belongs to( a ,b) so assume a,b are 4,8 and c is 2 and d is 6

Q: How many integers between 1 and 10000(inclusive) are divisible by at one of 9, 10, 11?

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Q: sum of two even integers is even

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Q: Prove, that (nezond n73) If x"=5,+hen x is not a rational number.

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Q: What is the set of O of odd positive integers less than 10?

A: The odd positive integers less than 10 are 1, 3, 5, 7, 9.

Q: Prove by contradiction that 2020 cannot be written as a sum of 3 odd integers.

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Q: Rprove that for ony natural number n, 2+4+ --

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Q: The ancient Greek were the first to insist on proofs for Mathematician statement to make sure they…

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Q: Show that if seven integers are selected from the first 10 positive integers, there must be at least…

A: We can solve this question by pigeonhole principle

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Q: Explain Cantor, of way 2. proving the set of algebraic numbers is countable Set.

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Q: Suppose that all the pages are black and white, but each group of 25 consecutivepages (1-25, 26-50,…

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