Determine the smallest integer that can be expressed as a sum of two primes in three different ways.

Q: plz solve q4

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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: pair of these integers with a sum equal to 9.

A: Let us take set under consideration {1,2,3,4,5,6,7,8}Possible pairs {{1,8}, {2,7}, {3,6}, {4,5}}…

Q: What is an integer

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Q: How many 3 digit even numbers can be created if repetition of digits is allowed

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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: When four positive integers are added three at a time the sums are 1551, 1659, 1720 and 1736. The…

A: when four positive integers are added three at a time the sums are 1551, 1659 ,1720 and 1736. we…

Q: Show that the sum of the cubes of the first n positive integers is (n(n + 1)/2)^2

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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 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: Let ab5c be all four-digit multiples of number 36 with different digits. If someone found 7 numbers…

A: Let ab5c be all four digit multiples number 36 with different digits.   As 36= 4x9, so the number…

Q: Find the number of positive integers not exceeding 1000 that are not divisible by 2 or 3 but…

A: The positive integers not exceeding 1000 that are not divisible by 2 or 3 but divisible by 5 are 5,…

Q: Show that 3 + V5 is inational number

A: Let 5^1/3 is a rational numbers. So, we can write it as 5^1/3=p/q ………….(I) according to the…

Q: Show that if any eight positive integers are chosen, two of them will have the same remainder when…

A: Pigeonhole Principle- If n items are assigned to m containers, and m<n,then at least one…

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: What is the units' digit of the sum of the squares of the first 2019 odd positive integers?

A: To find the sum of squares of the first 2019 odd positive integers.

Q: At the end of 2005, the largest known prime number was 2^30402457 -1, write an expression for the…

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Q: All composite number can represent as product of primes numbers

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Q: How many 5–digit (decimal) integers are there with none of the digits repeated?

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Q: a number whose decimal reoresentation repeats is a rational number. true or false

A: A number is rational if and only if its decimal representation is repeating or terminating (i.e.…

Q: How many mombers between 50 and 200 can be expressed as 4k-1, where k is an integer?

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Q: What is the sum of the first 150 positive integers?

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Q: What is the sum of the first 200 positive integers?

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Q: Show that 2 + V5 is imational number

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Q: (b) Find the sum of the first 110 positive odd integers.

A: Our Aim is to find the sum of the first 110 positive odd integers.

Q: Find the sum of all integers that are multiples of 3 from 4 to 100.

A: We have to find the sum of all integers that are multiples of 3 from 4 to 100 Then, If A denotes the…

Q: The number of positive integers not exceeding 750 that are divisible by 3. 4. and 7 is: *

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Q: Find the sum of first 30 positive integers divisible by 6

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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: In a large math conference with 2022 participants, each person shakes hands with some number of…

A: For 'n' number of participants the maximum number of handshakes is n(n-1)/2.

Q: What is the sum of the first 100 nonnegative integers?

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Q: How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0 if…

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Q: what is the smallest positive integer greater than 1 that divides the number 7^2021-13^2021

A: here 7×2021-13×2021  =2021(7-13)                                       =2021(-6)…

Q: The total number of positive integers that can be formed from the digits 1,2,3 and 4 if no digit is…

A: Number of possible arrangement can be calculated either by combination or permutation methods.…

Q: Find all primes that divide 50!

A: Solution:-

Q: How many even three digits numbers can be found from the digits 3,2,5,6 and 9 if each digits can be…

A: Given, s={3,2,5,6,9}

Q: What is the smallest sum possible sum of 25 consecutive positive integers which s a perfect square?

A: Let's take the 25 consecutive positive numbers as an Arithmetic Progression with first term a.…

Q: Determine the possibilities for the final digit of a sixth power of an integer.

A: The last digits of a number are 0,1,2,3,4,5,6,7,8 and 9. The number 0 raised to any number will be 0…

Q: Find the number of positive integers not exceeding 120 that are divisible by 3 or 4

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Q: Show that every odd integer is the difference between two consecutive perfect squares.

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Q: How many twin primes are there where both primes are less than or equal to 31? Number of twin…

A: Twin prime: If there is only one composite number between two prime numbers, then that two numbers…

Q: Find the number of positive integers ≤ 1000 that are not divisible by 5, 13, or 31?

A: .  Symbol of Greatest Integer Function  To Find: Number of positive integers ≤ 1000 that are not…

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: The chairs of an auditorium are to be labeled with a letter and a positive integer not exceeding…

A: Given: The chairs of an auditorium are to be labeled with a letter and a positive integer not…

Q: What is the sum of the first 9,000 positive integers

A: topic - arithmetic sequence answer is 40504500

Q: How many positive integers not exceeding 100 are divisible by 5 or 7?

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Q: How many corresponding integers are made up of 1443 digits taken from (1-2-3-4-5-6) provided that no…

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Q: What 2 nonnegative numbers with a sum of 23 have the largest possible product?

A: Given information: The two non negative numbers with a sum of 23.  Calculation: Consider x and y are…