Prove that if q^2 is divisible by 3, then q is divisible by 3.

Q: Show that quaternion multiplication is not commutative. (That is, give an example to show that…

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Q: Prove that 2n32n - 1 is always divisible by 17.

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Q: Show that 2^645 -1 is a pseudoprime. i know 2>1 and 645 is composite. But how to prove 645 divides…

A: A pseudoprime or probable prime is actually not a prime number or it is a composite number which…

Q: What is the remainder when 2021202120212021 is divided by 2020? use congruence modulo

A: a = 2021202120212021 b = 2020 If a = qb + r then  a ≡ r mod n.

Q: In the expansion of + 6)-", state the number of terms and the coefficient or the middle term. 21, 20…

A: Introduction: The binomial expansion is a very important finite series in mathematics. With the aid…

Q: o use divisibility in this problem but i am not sure where to start. Prove or disprove (with a…

A: Introduction: If a and b are integers, a divides b if c is an integer and ac = b. The symbol a|b…

Q: Find the smallest integer greater than 100 that is divisible by 3 but leaves the remainder 1, 5 when…

A: Let x be the required number. The number is divisible by 3, so it leaves the remainder 0 when it is…

Q: Give a combinatorial interpretation of the coefficientof x6 in the expansion (1 + x + x2 + x3 +⋯)3.…

A: According to the given information, it is required to give a combinatorial interpretation of the…

Q: Use mathematical induction to prove that +1+2+4+...+2"-² = 2"- for all 2 -- positive integers . п.

A: We need to prove using mathematical induction given statement First we will show statement holds for…

Q: Prove that 279,930 is divisible by 7 using Fermat's Little Theorem.

A: We have to prove that 279930 is divisible by 7 using Fermat's Little theorem. The Fermat's little…

Q: Prove that for all integers, n , n^3-n is divisible by 3.

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Q: If 17th term of an AP exceeds its 10th term by 7 , Find the common differenc

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Q: Expand with help of Binomial Theorem (- +)

A: Using the Binomial theorem, the binomial expansion formula for (a+b)n is given by the formula,…

Q: Use Fermat’s Little Theorem to prove that 8^46 − 1 is divisible by 139

A: Use Fermat’s Little Theorem to prove that 8^46 − 1 is divisible by 139

Q: Suppose each license plate in a certain state has two digits, followed by two letters, followed by…

A: Given,no.of letters=24no.of digits=10

Q: Show that every positive integer can be written as the product of a square (possibly 1) and a…

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Q: how do you find "In (5/2) " on a calcualtor

A: To find ln(5/2)

Q: Suppose each license plate in a certain state has three letters followed by three digits. The…

A: * License plate must have       3 letters and 3 digits ; repetitions allowed.Also , letters H and L…

Q: 9.) Is 9" + 3 is divisible by 4? PROVE IT!

A: Given : 9n+3 is divisible by 4. To Prove: The given statement is true for n=k+1. Consider Tn=9n+3.…

Q: divisible by 3 for

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Q: Which term of the expansion of (x° + 7) contains x 28 ,36 Term number contains æ36

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Q: Show that 4(44!) + 49 is divisib by 47

A: Given: To show that 4(44!)+49 is divisible by 47. To explain the given statement as follows,

Q: Number 3^32 -1 has exactly two divisors greater than 75 and less than 85. What is their product?

A: Use the exponential property, abc=abc to simplify the given expression. It is known that an-bn is…

Q: Find the number of strings of length 8 of lower case letters of the alphabet, with repeated letters…

A: The length of the string is 8 and one letter are given , begin with v or end with f. We have to…

Q: Prove that AXB|=A²B² - (AB)².

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Q: Prove a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

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Q: Show that n-lis divisible by 8, if n is an odd positive integer

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Q: Evaluate (521 + 3z2)

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Q: Prove that the product of an even number and an odd number is even.

A: Here, objective is to prove that the product of an even number & an odd number is even

Q: Describe a general method for finding all the divisors of a positive integer once you know the prime…

A: Given  A positive Integer whose prime factorization is given . To find all the divisors with general…

Q: The greatest common divisor of two number 1, b(nteger) are. None of the

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Q: SHOW THAT 3^2N - 1 IS DIVISIBLE BY 8 FOR ALL POSITIVE INTEGERS.

A: We prove this by induction.

Q: Find the recursive and explicit rule for -1, 3, 7, 11,... Recursive rule

A: This is a problem of series . Based on concepts and formulas we will answer the question.

Q: Prove: The product of 2 numbers is equal to the product of their least common multiple and their…

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Q: Are the rest of division of Euclidean method to give the GCD(351,231): o 351, 231, 120, 111, 9, 0 o…

A: GCD = Greatest common division

Q: find all three-digit number with different digits with the property that those numbers are divisible…

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Q: 2. Show that 1184 – 534 is divisible by 7. -

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Q: divisible by 3

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Q: "For all integers n, n(n² – 1) is divisible by 6." (You may use quotient-remainder theorem and…

A: Let us consider, for all integers n a = n3 – n a = n (n2 – 1) a = n (n + 1)(n – 1)

Q: Use binomial theorum to expand (1 + 1/x)^7

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Q: Prove that a natural number (an-1an-2a1ao)10 is divisible by 9 if and only if the sum of the digits…

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Q: 4503 is divisible by 2,3,,5,6,9or 10

A: 4503 is divisible by 2, 3, 5, 6, 9 or 10.

Q: (2) Explain why the rational numbers are those having periodic representation or with- out infinite…

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Q: Find the product of - 10 - 6i and its conjugate. Question Help: DPost to forum

A: Given -10-6i

Q: Put a positive whole number in each of the four boxes of this table that satisfies the rule. For…

A: Prime number is a positive integer having exactly 2 factors. for example 7 is a odd prime number as…

Q: Number 332 – 1 has exactly two divisors greater than 75 and less than 85. What is their product?

A: We need to find two divisors of 332-1 between 75 and 85.  Now, we can use the identity a2-b2=a-ba+b…

Q: Prime divisors of two numbers a and b are 2,3 and 5 and product of these numbers a and b is 5400.…

A: The prime factors of the two numbers are 2, 3, and 5 and the product of these two numbers is 5400.

Q: 9. Prove that the greatest common divisor of two positive integers divides their least common…

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

A: To determine the number of ways for the 125 pages to assign to the 5 printers. Given that, the total…