ere exists an integer a with 9p +1 = x³. Let n be an integer. Show that if 2 + 2/1+ 12n² is an integer, then it is the square an integer.

Q: Select two positive integers a and b with 5 <  a  ≤  20  and 5  <  b ≤  20.

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Q: Problem 4 [25 points]: Contradiction Given a proof by contradiction of the statement: If n? + 11 is…

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Q: find a Positive integern for which the equality holds %3D

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Q: Show that if a positive integer is odd, then it's square is odd.

A: To show that if a positive integer is odd then its square is odd

Q: Prove that 5 does not divide 5n+3 for any integer n.

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Q: Prove that a number in the form 6k+5,” what I mean is a number in the form of 6 times some integer…

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Q: Step by step else downvote, with clear handwriting. Prove that for any real number x, there exits a…

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Q: Show that if n is any integer, then 3 divides n3 − n

A: To prove:  if n is any integer, then 3 divides n3 − n. Concept used: Here we shall use the identity:…

Q: (b) Prove that any odd number is expressible in the form 4n + 1 or 4n + 3 where n is an integer.

A: Number System

Q: at any positive odd integer is of the

A: Here we have to show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5,…

Q: Prove that for a positive integer n we have that 33n+3 – 26n – 27 is divisible by 169. - -

A: The given expression is: 33n+3-26n-27 This is to be proved that the expression is divisible by 169.

Q: Given any real numbers a and d, consider the expression (a + md) + (a + (m + 1)d) + (a + (m + 2)d) +…

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Q: Disprove the statement: There is a real number x such that xº +x* +1 = 2x².

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Q: 1. Prove that the sum of an integer and its square is even

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Q: (d) (11 × 14" + 1) is a composite integer for every positive integer

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Q: Prove that the sum of the squares of two odd integers cannot be the square of an integer.

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Q: Prove that 67n+ 17 cannot be a perfect square for any three consecutive integers n.

A: We will use quadratic residue and proof by contradiction method.

Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

Q: 6. Letn be a positive integer. Prove that 1+ 4+7++ (3n − 2) = = 3n² 2

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Q: "Every positive integer can be written as the sum of the square of 3 positive integers." prove…

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

Q: Show that if k is a positive integer, then (15k+4)/(10k+3) is in lowest terms.

A: We use the concept of Ring theory that a fraction is in lowest form if the gcd of numerator and…

Q: - 5. Prove that an integer n is odd if and only if n° – 3 is even.

A: Answer

Q: I need help

A: To find:∫013481-u221+u23du

Q: For positive integers a and b, show that a ab

A: Consider the provided question, For positive integers a and b,  we need to show that, xab=xab

Q: (d) Prôvé that the square of every prime number greater than 3 is one more than a multiple 24.

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Q: Find an odd integer o written as an expression using the variable k with the property that when f is…

A: Here we have given a mapping  which proves that both the sets have same cardinality.

Q: Find all sollutions in integers of 34x+8y=6

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Q: Let n be an integer, use the definition of even to prove that 10n+ 4 is even. 10n+4=0x0 Since is a…

A: Let n be an integer. To prove that for any integer n the number 10n+4 is even. An even integer is…

Q: Show that V3 +2/6 is an irrational number.

A: A rational number can be represented as pq, where p, q are integers and q≠0. If a number can not be…