Find the six smallest even perfect numbers.

Q: are there any even numbers greater than 2 which are prime? why or why not?

A: We will find the solution in the following step

Q: Why k(k+1) is an even number?

A: We have to tell just  that why k(k+1) is an even number.Here we considering that you understood  the…

Q: 1) Show that the square of an odd integer is odd. 2) Show that the product of two odd integers is…

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Q: How many 10 digit real even number can be created (It cannot start with a 0) with 5 zeroes and 5…

A: Basic concepts of making combination are used. Information given, As we have only two choices of…

Q: Show that a number with 30 digits cannot have more than 100 prime factors.  

A: Prime factor: A factor of a number which is a prime number. For example: consider a number 26. The…

Q: Find the smallest number n for which n! is larger than the population of the world.

A: World population is 7.98 billion till October 2022 It according to worldometer by United States.…

Q: Use any method, list all the three digit numbers from the set {3,4,5,6} where there are no repeating…

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Q: ll integers are rational numbers

A: All integers are rational numbers

Q: Find all integers n > 1 such that 1n − 1)" is +2+...+(n divisible by n.

A: To find all the integers n>1 such that 1n+2n+...+n-1n is divisible by n

Q: How many 6-digit numbers have three even and three odd digits? (The first digit cannot be zero.)

A: It is given that a 6-digit number is to be formed which will have three even and three odd digits.…

Q: prove that the sum of three odd integers is odd using indirect method. show your solution and…

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Q: A girl writes a different natural number on each of the cubes in the image. The sum of numbers on…

A: For maximizing a particular number in an equation, try minimizing other numbers. By doing this…

Q: What is the largest number x such that x<200 and x has exactly 4 factors?

A: Factors:    Number that are multiplied together to get a product                              Factor…

Q: 5. Consider the subtraction problem "6 - "13. a. Show how to represent the problem on a number line…

A: 6a)

Q: what two consective odd integers have a product of 63?

A: Find two odd integers.

Q: Find the smallest five consecutive composite integers.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT How many positive integers n ≤ 1000 are coprime with N=90

A: We know that 90=2×32×5 Numbers less than 1000 which are divisible by 2 =10002=500 Numbers less than…

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: Prove: “The sum of two even integers is even.”

A: To prove: The sum of two even integers is even. n is an even number if it can be expressed as n =…

Q: identify all natural numbers having exactly 28 divisors.

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Q: 3. Show that there exist 100 consecutive positive integers that are not perfect squares.

A: Here we have to show that there exists 100 consecutive positive integer that are not perfect square.…

Q: Eleven friends stand in front of an elevator that has a maximum capacity of 10 people, so up to 10…

A: given that there are 11 friends stand in front of an elevator. but the elevator has capacity of 10…

Q: 9) The dimensions of a gift box are consecutive positive integers such that the height is the least…

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Q: Find all primes that divide 50!

A: Solution:-

Q: If P is a prime number &gt;2, will P+7 ever be prime? Why or why not?

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

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