a) If a| (21b−c) and 6c≅3b(mod2a), then a| 41c b) If a≅b(modc) and d|c then ?≅?(mod?) c) ∴(d| (ab+c) & d| b) <--> (d| b & d| c)

Q: Prove that Va - Vb is irrational number if 'a' and 'b’ are prime number?

A: Given To prove that a-b is irrational number if a and b are prime number.

Q: Let x be an integer. Prove that, if x mod 9 = 5, then 9|(x^2-2x+3)

A: Given: x mod 9=5 then, 9|x2-2x+3|

Q: I don't understand why 3n+2 is congruent to 2n+1(modk) and 3 is congruent to 2(modk). Please…

A:

Q: For a natural number n, we define n! = 1-2-3 (n − 1). n. - For example: 2! = 1-2, 3! = 1-2-3 = 6,…

A:

Q: Prove or Disprove: |Q| = |Q^200|, where Q is the set of rational numbers.

A:

Q: + 220 + 330 + 440 + 550 + 660 (

A:

Q: 37x = 101 (mod 151)

A:

Q: Prove or disprove the following statement: There are prime numbers a, b, c such that a^2+ b^2= c^2.

A:

Q: Prove (kindly provide reason/s) that for any real numbers m and n, (-m ) + ( - n ) = - ( m + n)

A:

Q: (a) Show that, for any odd prime p > 5, 1 if p = 1, –5 (mod 12) (주) -1 if p= -1,5 (mod 12)

A:

Q: SuPpose that15,000 is invested in a savings account that earns i) Find an expression for the amaunt…

A: $15,000 is invested in a savings account that earns 4% interest, compounded quartely.

Q: Prove a^2 +4a+3 is odd if and only if a is even.

A:

Q: Prove by cases For any integer n, n^2 + 5 is not divisible

A:

Q: ), c= 9) [1 2] A B = 8 3. ]

A: Topic- matrix multiplying

Q: Identify if the given statement is true or false: I. If a is an integer, the (a^2 is congruent to 0…

A: Given some statements. Check whether these statements are true or false.

Q: Prove a2 = c² (mod n), assuming that a, c and n are integers with n > 1 and that a = c (mod n)

A:

Q: If a and b are integers with gcd(a, b) = d Then gcd d' = -1 d/

A: Given a statement

Q: 5) Let n be a positive integer such that 7 | (8-1). Prove that 7 | (8=*1 - 1). (Hint: Rewrite 8*1…

A: Given: Let n be a positive integer such that 78n-1. To prove: 78n+1-1

Q: Calculate the right hand side of the statement below for n=12 ©George Mason University 3+4+5+. + (n+…

A:

Q: For all integers n, if 6 | n, then 9 | ((n^2) + 21n/2)

A:

Q: If O is a natural number then O^2 + 2O + 1 is odd.

A: If O is a natural number then we need to check whether  O^2 + 2O + 1 is odd. The result is given…

Q: If a and b are integers with gcd(a, b) = d Then a gcd %3D -1

A: False.

Q: Show that this number is Irrational number

A:

Q: fermat's theorm states, if p is prime & a is a positive integer not divisible by p then-------- and…

A: Fermat's Theorem: If p is a prime and a is a positive integer and not divisible by the prime p, then…

Q: x² + x = 13(mod17) X= * (mod17)

A:

Q: fermat's theorm states, if p is prime & a is a positive integer not divisible by p then-------- and…

A: Fermat's states that if p is a prime and a is a positive integer not divisible by p, than ap-1≡1 mod…

Q: One of the striking properties of Fibonacci numbers is that gcd(Fm, Fn) = Fd, (*) where d = gcd (m,…

A: 1. We see,        F9 = 34    [Fibonacci series : 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,. . . . . ]…

Q: Simplify (15-54)(mod 4). (15-54)(mod 4) =(mod 4)

A: Simplify          (15 - 54)(mod 4)

Q: Is 17 congruent to 4 modulo 6.

A: 17, when divided by 6, leaves remainder 5

Q: Q020 til Jistil= a Evaluate +Re(

A: We need to evaluate the integral, ∫z+i=2z+i2020+Re(z) dz. So, ∫z+i=2z+i2020+Re(z)…

Q: Find oll integers Such thot 24! x =1 Cmod 2) 5x = 3. (mod 8) and 1500 < X <2000

A:

Q: Let a, b and c be integers that satisfy 1 1 1 - - - - a b C |(A) 2022 (В) 2025 Find one possible…

A:

Q: • Show that if m divides 3, then m divides 9. (We say a divides b if there exists an integer k such…

A: Let  m divides 3 .  Then there exists an integer k such that 3 = mk. Now, 9 can be written as…

Q: Suppose that b and c are integers where 9b = 12c. Then 9|c and 12|b.

A:

Q: prove that Every positive integer n can be written as n =( 2^a)(5^b)c, where c is not divisible by 2…

A: Fundamental Theorem of Arithmetic: Every positive integer (except n=1) can be uniquely expressed as…

Q: Simplify (98 +31)(mod 7).

A: To simplify (98+31)(mod7), first perform the addition inside the parentheses and then find the…

Q: Please provide justified answer asap:::: Show that n is odd if and only if n^2+4n+1 is even.

A:

Q: If 3x = 6 mod 9, when -2 <x< 8. Then O x=(-1, 3, 5} x=(-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

A:

Q: Show that Consider the Fibonacci numbers {F} defined by F₁ = 1, F₂ = 1, and Fn+2= Fn+1 + Fn. - Fn =…

A: Introduction: In mathematics, a recurrence relation is a significant connection that expresses the…