) Find an integer having the remainders 3, 11, 15 when divided by 10, 13, 17, respec- tively. (Regiomontanus, 1436–1476).

Q: Determine whether there are infinitely many primes that have a remainder of 12 when divided by 25.…

A: Given question is Determine whether there are infinitely many primes that have a remainder of 12…

Q: The number of factors of prime numbers are None of the mentioned O 30 Depends on the prime number

A: No. Of factor of prime no. Means how many divisor consist of a prime no.

Q: What is the converse of: an integer has divisors other than 1 and itself, if an integer is…

A:

Q: Find the least positive integer that yields the remainders 1, 3, and 5 when divided by 5, 7, and 9,…

A:

Q: The number of factors of prime numbers are Depends on the prime number None of the mentioned (3 2

A: Given query to find number of factors of a prime number.

Q: Find the smallest positive integer that leaves a remainder of 1 when divided by 2, a remainder of 2…

A: Let N be such a number N=10a+9:  N+1 = 10a+10 N=9b+8: N+1 = 9b+9 N=8c+7: N+1 = 8c+8 N=7d+6 and so on…

Q: The number of factors of prime numberss are (None of the mentioned Depends on the prime number (2 (3

A: Prime number is only divisible by 1 and that number itself

Q: Use ibn al-Haytham's procedure to derive the formula for the sum of the fifth powers of the…

A: We have to derive the formula 15+25+......+n5=n66+n52+5n412−n212 by using ibn al-Haytham's method…

Q: The notions of the greatest common divisor and the least common multiple extend naturally to more…

A: Suppose we have three positive integer a , b and c where a=p1x1·p2x2·⋯⋯ ·pmxm , b=q1y1·q2y2·⋯⋯ ·qnyn…

Q: If p + 2 is a prime number, prove that p² + 3 is divisible by 4.

A:

Q: in pascals triangle which row has a sum of 65536?

A: We know that the sum of every row of Pascal's triangle is twice of the last row's sum.  And it is…

Q: The Great est Common Divisor of two prime numbers a and b is

A: Given : a and b are two prime numbers To find : Greatest Common Divisor of a and b.

Q: The integers 77 and 105 are relatively prime.

A: Relatively Prime integers: Two integers mand n are called relatively prime if gcd(m,n)=1. Given two…

Q: What is the smallest positive integer that has 6, 8, and 10 as factors?

A:

Q: Show that if 5 divides n2 with remainder 4, 5 divides 3n3 with remainder 2.

A: Given that 5 divides n2 5 n25 n×n5 n5 n3 As it gives the remainder 4 on dividing by 5. Therefore it…

Q: Show by mathematical l Induction y 4n-2 3. +17 can be divided by +22 possitive integers 16 far all

A: To prove the given statement by using mathematical induction.

Q: The integers 77 and 105 are relatively prime. صواب İhi

A: By finding the factors of given numbers you can find the solution :

Q: 1. What are the possible remainders of prime numbers greater than 2 when it is divided by 7? а. 1,…

A:

Q: 1- Show that if a is an integer, then 3 divides a^3-a. with details plz

A:

Q: If the product of two integers is 2'3*5?7!" and their great- est common divisor is 2°345, what is…

A:

Q: If n = p,P2 ... P where the p, are distinct prime numbers, how many ways can n be written as a…

A: First let us formulate the problem in a different way. Look! we have to find the total number of…

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

A:

Q: Every odd prime number is greater than 2.

A: Given: "Every odd prime number is greater than 2." To find: Statement in the form "If p, then q"…

Q: 3. The GCF of any two distinct prime numbers is 1. (Distinct they are not the same number) means

A:

Q: Prove or disprove: If an integer is divisible by 6 and by 10, then it is divisible by 60.

A: Answer

Q: Suppose “a” is an integer. If 5|2a, then 5|a.

A:

Q: Prove in a thoroughly written proof that for all integers a  and m, if a and m are the lengths of…

A: Recall the following. Pythagoras theorem: For any right triangle, the square of the hypotenuse is…

Q: 4. Prove that the cube of any integer can be written as the difference of Notice that squ n³ = (1³ +…

A: To prove that cube of any integer can be written as the difference of two sqaures.we have given hint…

Q: Find the largest valuc of integer value ofk such that 1 (24 - 1) < 900. 5+7++

A:

Q: The positive integers that are divisors of 68 are

A: We will use multiple method to find all the divisor of the given number .

Q: А. If p 2q 5 is a prime number, prove that p2-q? is divisible by 3.

A:

Q: 3. Use Euler's Theorem (and the Chinese Remainder Theorem) to how that n12 = 1 (mod 72) for all (n,…

A: The Euler's Theorem states that for a positive integer n and an integer a that is relatively prime…

Q: Find all prime numbers pand of for which 2p²q + 45 pp ² = y² 2 де

A: Given:

Q: Find the largest negative integer leaves a remainder 2 when divided by 3, 5, and 12. (If it is not…

A: Let us  solve the question in the next step.

Q: For the rimbIS 588 and 2520 -FaCtor each nmbor into a pnduct 1Of Primes in carionicat tom.

A:

Q: Prove: If the sum or the difference of two irreducible fractions is an integer, the denominators of…

A: Proof: Let two irreducible fractions are ab and cd Since the fractions are irreducible, (a,b)=1 and…

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: How many zero divisors are in Z,, where n = 32547?

A:

Q: Sort the numbers 10 to 30 in each Carroll diagram. Multiples Multiples of 3 Multipl of 4 of 3…

A: Corrall diagram is a way to organised the information according to the rows and columns of the given…

Q: Show that the sum of twin primes p and p + 2 is divisible by 12, provided that p> 3.

A: Let p, p + 2 be twin primes. Then p *(p+1) + 1 = p^2 + 2p + 1 = (p+1)^2 ,  a perfect square.

Q: Suppose that p is a prime number greater than 30. Prove that when p is divided by 30, the remainder…

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Q: find the sum of all integers between 300 and 800 that are exactly divisible by 14

A:

Q: 8. Show that no prime number of the form 4k +3 can divide a number of the form n2 + 1.

A:

Q: Assuming every integer is either even or odd, How would I show that for any integer, the difference…

A: Assume that every integer is either even or odd. Let the integer considered say x is even. Then by…

Q: The notions of the greatest common divisor and the least common multiple extend naturally to more…

A: Given: a=21·32·72b=23·33·71c=31·52·73

Q: If X is a positive integer divisible by 6, and X <60 What is the greatcst possibe vaive of X 7

A:

Q: A restaurant sell features a burrito bar in which a customergets to choose one of 2 different kinds…

A: As per bartleby guidelines only one question is answered please upload the other one separately…

Q: Show that 19 divides 10*8n-1 + 33n-1 for every positive integer n.

A: Concept: Mathematical induction: For each and every natural number n, mathematical induction is a…

Q: 1.What is the smallest number that can be exactly divided by 2, 3, 4, 5  and 8 ? 2.What are the…

A: To answer the given questions.