Use these sum of even integers: 6 +26 = 32 4+ 24 = 28 Conjecture: the sum of any two even integers is 12+ 10 = 22

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

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Q: 7p The simplified product of 5m³n3 and p5 where m + 0, n # 0 and 10m4n p + 0, can be represented by…

A: We have to simplified the product.

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

A:

Q: 4 (ii) 16 | at + 15.

A: Step-1 1)16|a4+15

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: 51|1032n+9 – 7, for any integer n 2 0. O True False

A:

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: How is duality connected to the principle of reciprocity in number theory?

A: To find: How is duality connected to the principle of reciprocity in number theory.Duality and the…

Q: Prove the following: There exist no integers a and b for which 14a + 4b = 1. Please explain the…

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Q: (b) If a, b and c are integers such that b| a and b| c, then b | (2a – 3c).

A: We have to proof

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

A:

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

A:

Q: Show that x2 + 9 is prime.

A: To show x2 + 9 is prime.

Q: Prove or disprove: There exists an integer a such that 14 | (3a – 5) and 21 | (2a +3).

A:

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: "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: what are integers ?

A: An integer can be described in simple words as a whole number with negative and positive sides. You…

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: 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…