Fermat's theorem is not true for some prime number. Select one: O True O False

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

A: Let p≠2 be a prime number.

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

A: Prime numbers are the numbers which have only two factors one factor is 1 and other factor is 2

Q: The square of an even integer is congruent to 0 (mod 4). Select one: O True O False

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

Q: Find the greatest natural number n such that n + 10 divides nº + 100.

A:

Q: Let p > 5 be the prime number. Prove that the expression p – 10p +9 is divisible by 1920.

A: We have to prove that the expression p4-10p2+9 is divisible by 1920.

Q: Determine whether the following statement is true or false. Justify your answer with a proof or a…

A:

Q: Want a rigorous proof   Prove that The set of prime numbers has no largest element.

A:

Q: Justify that every prime number except 2 and 3 has the form 6q + 1 or 6q + 5 for some integer q.

A: Let p be a prime number other than 2 and 3. If p is divided by 6, then by the quotient-remainder…

Q: Fermat's theorem is not true for composite number. Select one: O True O False

A: Ans :  true

Q: Every natural number can be written as the products of prime numbers

A: Prime numbers are the numbers which have only two factors, 1 and the number itself.

Q: Show that if n is any integer, then 3 divides n3 − n

A: To prove:  if n is any integer, then 3 divides n3 − n. Concept used: Here we shall use the identity:…

Q: Show that an integer N is divisible by 9 if and only if the sum of its digits is divisible by 9

A: Let a=anan-1...a3a2a1 be an integer and S be the sum of the digits. Consider a,…

Q: Every natural number greater than 1 can be written as the products of prime numbers.

A: Prove that  every natural number greater than 1 can be expressed as product of primes or the number…

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

A:

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: p + 2 is a prime number, prove that p2+3 is divisible by 4. (2.5

A: Prime and divisibility

Q: Find the smallest positive integer N that satisfies all of the following conditions: • N is a…

A: We have to find the smallest positive. N'that satisfies all of the following conditions: N is a…

Q: Every two different prime numbers are relatively prime. False True

A: In this question we need to check the given statement is true or false

Q: All prime numbers are odd.

A: We have state whether given statement is True or False. We know that  A prime number is a number…

Q: Which positive integer less than 21 are relatively prime to 21? 21 (24 (19 (18

A: Relative prime are those numbers which does not have any common factor and HCF is 1

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: Is the conjecture "all prime numbers are odd" true or false? O True O False

A:

Q: There exist two prime numbers and such that their product gives 1261

A: We have to find two prime numbers whose product gives the required number

Q: Show that if n is a positive integer then =n(n + 1)2"-2

A: We know the binomial theorem formula isx+yn=∑k=0nCkn xn-kyk, where Ckn is the binomial co-efficient…

Q: Which positive integer less than 21 are relatively prime to 21? 18 O 19 O 21 O 24 O

A: Which positive interger is less than 21 is relatively prime to 21?

Q: Use indirect proof to show that if n is an integer and n^3 + 5 is odd, then n is even.

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: prove that the one's digit of any integer,n, is the remainder when one divides n by 10.

A:

Q: Determine how many ti (o bom is a prime.

A: In this question, the number of times is determined when 1 appears in the multiplication table for…

Q: 5. Use the direct proof to show that " If n is an odd integer, then n2 + 3 is even

A:

Q: If a, b, c, d are distinct prime numbers with an as smallest prime then a *b * c dis None of the…

A: Answer

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

A: Answer

Q: how many pairs of primes p and q are there such that q-p=3? Prove your answer.

A: Here, we need to find all the possible pairs of prime numbers p and q such that the difference (q-p)…

Q: describe (a,p)

A: Given, if p is a prime, and a is a positive integer.

Q: True/False: Every integer greater than 1 is divisible by a prime number. True False

A:

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

A:

Q: show that no integer of the form n^3+1 is a prime other than 2

A:

Q: Prove that 2^(27) - 1 is not a prime number.

A: A prime number is a natural number greater than 1 that is not a product of two smaller natural…

Q: Which positive integer less than 21 are relatively prime to 21? 21 (24 (18 (19

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: If p2q25 is a prime number, prove that p-q² is divisible by 8.

A: Given, p≥q≥5 are prime numbers, Now, p2-q2=p+qp-q. Since, p and q are prime which are grater than…

Q: The number of primes of the form n³ – 1 is 1) 1 2) 2 3) Infinite

A: To choose correct option

Q: How many positive integers between 100 and 999 inclusive a) are divisible by 7? b) are odd? c)…

A:

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: What is the value of the smallest composite number with exactly 3 distinct prime num- ber in its…

A:

Q: Show that if a is a positive integer, then Lo-:(---) n(n +a) n=1

A: Let a is a positive integer, the term a can be written as a = n + a – n

Q: yields a true statement when n is replaced by any positive integer.

A: The above statement is true. Step-2 i explained in detailed explanation

Q: Every prime number is odd. True False

A:

Q: Every natural number n > 2 cam be writtenn = PiP2 Pr as the ... product of distinct prime numbers…

A:

Q: is a prime number and that n is an integer such that p|n^2 prove that it follows p|n

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.