Let "xy" denote "x does not divide y." Prove by any method. Let a and b be integers. If 3 ab, then 3a and 3 lb. Let a and b be integers. Suppose that 3 | a or 3 | b. If 3 | a, then a = and 3 b. for some integer k. Therefore ab = so 3 ---Select-- ab. Similarly, if 3 | b, then 3 | -Select-- ab. Therefore, by contraposition, 31 a

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

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Q: If a and b are integers, then a/b is always a rational number. True False

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

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Q: 4. The following table presents a sequence of algebraic expressions that have a logical sense. There…

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Q: snip

A: Given: A=2131-10 and B=102132   (a) To find: AB

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

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

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 1+6x-x is always a positive real number if x =3+Ai for some real 33 number 4

A: The given number is  1 + 6x - x2

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

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Q: Show that x2 + 9 is prime.

A: To show x2 + 9 is prime.

Q: Express numbers in exact form. Use symbolic notation and fractions where needed.) Jul =

A: From the dot product of two vectors  u.v=uvcosθucosθ=u.vv which is the projection of vector 'u'…

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: Show that 2 + V5 is imational number

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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…

Q: a.Given an integer a, then a² + 4a + 5 is odd if and only if a is even. b. There exists a positive…

A: Since you have posted multiple subpart questions, we will solve the first three questions for you.…

Q: **2.) In the diagram below, ray NK bisects JNL MJNK-(22-2 and MELNK-(3x)". Determine the value of…

A: Given: In the diagram, the ray NK bisects ∠JNL. m∠JNK=2x2-2°. m∠LNK=3x°. Since the ∠JNL is…

Q: ind p hat if x is 7 and n is 10

A: The provided information are: Number of success (x) = 7 Number of trials (n) = 10

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

A: Fermat's states that if p is a prime and a is a positive integer not divisible by p, than ap-1≡1 mod…

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

A: Answer

Q: Justify whether it is true to say that -1, - 2, .. forms an AP as a, - a, az - a,

A: Here given sequence, a1=-1, a2=-32, a3=-2, a4=52, .......

Q: For any integers a and b, a + b ≥ 15 implies that a ≥ 8 or b ≥ 8.

A: Let a+b≥15, where a,b are integers.   Case 1: b&lt;8 Then: b&lt;8⇒-b&gt;-8⇒15-b&gt;15-8⇒a≥15-b&gt;7…

Q: • Show that if m divides 3, then m divides 9. (We say a divides b if there exists an integer k such…

A: Let  m divides 3 .  Then there exists an integer k such that 3 = mk. Now, 9 can be written as…

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: Let * be the operation on the set of real number defined by a * b = 2a + 4b – ab. (a * b) * c = А.…

A: Operation * is defined by a*b=2a+4b-ab for all real number we have to find the value of (a*b)*c…

Q: 2""(-1)" +1 2. Prove that 1-2+2² – 2³ +...+(-1)" 2" =- for all positive integers n.

A: We prove this result by using mathematical induction. For answer please look at step 2.