4. Find 2001 (mod 205). (Enter the least non-negative integer

Q: c1x1(a) + c2x2(a)+ . . . +cnxn(a) = x(a). Let X (t) be the n x n matrix with column vectors x1, x2,…

A: Given : Xt be any  matrix of n×n           : c be column with component c1 ,c2 , . . .  . . .  ,cn…

Q: 16 M = 7 -5 Find formulas for the entries of M", where n is a positive integer. M" =

A: We have to find the entries of matrix Mn.

Q: Bwalya was born in 1980. In two leap years to come, Shabalala was born. In which year was Shabalala…

A: Given, Bwalya was born in 1980. We know that 1980 is a leap year. Also, we have a leap year come…

Q: How many positive integers less than 10000 are there which contain at least one 7 or at least one 9…

A:

Q: Find the smallest positive integer n such that 5 (3² +2²) (3ª +2¹) (3³ +2³)... (3² +22") > 9256

A:

Q: 32. Prove that 3 divides n³ +2n whenever n is a positive integer.

A:

Q: Find the number of positive integers X smaller than 12849 which have exactly 2022 positive divisors

A: Theory : Total no of divisor of a number, If its prime factorization, given by ∏i=1hpiai Where p is…

Q: Show that if a positive integer is odd, then it's square is odd.

A: To show that if a positive integer is odd then its square is odd

Q: Prove that 5 does not divide 5n+3 for any integer n.

A:

Q: 16. All positive integers with negative squares are prime.

A: It is a statement. And it is  vacuously true.

Q: (b) Prove that any odd number is expressible in the form 4n + 1 or 4n + 3 where n is an integer.

A: Number System

Q: If fN is the set of the first 100 positive integers, A is the set of odd numbers between 50 and 90,…

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

Q: 5. Show that 2 32 3" 31 3" for all positive integers n.

A:

Q: Prove that, all integers x and y, x^2-4y≠2  1a. Prove that all numbers of the form 1007, 10017,…

A:

Q: Which positive integers less than 20 are relatively prime to 20?

A:

Q: Let a > 0 be a real number and I = [" LL* rdzdrd0. Then I = 2па 4па па None of these

A:

Q: 4. >2 1+ 100 1-0,9* >0,8

A:

Q: Prove that the sum of any five consecutive positive integers is always a multiple of five.

A:

Q: Let k be an positive integer. Prove that k(7k^2 + 5) + 6 is divisible by 6

A: Let k be an positive integer. Prove that k(7k^2 + 5) + 6 is divisible by 6

Q: Suppose that 75% of students attend lectures for a particular course and 20% of students fall the…

A: Conditional probability : Conditional probability is a measure  of the probability of an event…

Q: How many integer solutions to x1 + x2 + x3 + x4 x₁ ≥ 4, x2 ≥ 2, x3 ≥ 5 and x4 ≥ 3? > = 31 are there…

A: Find change all inequality to grater then equal to 0. Then use the theorem

Q: What is the last ans

A: 64% of all students at a college still need to take another math class. i.e., p=0.64"…

Q: Find all the values of x such that X 4²x17 * 4 + 16 = 0

A:

Q: Find the final amount of money in an account if $7, 600 is deposited at 6.5% interest compounded…

A:

Q: 2. Prove that the difference of an odd integer and an even integer is odd.

A: Prove that the difference of an odd integer and an even integer is odd

Q: Prove that 6">5" + 9 for any integer n ≥ 2.

A: Mathematical induction is a technique used to prove statements about well-ordered sets of natural…

Q: Let a, b, c be positive integers such that a is a multiple of c and a2 + b2 is not a multiple of c.…

A: a, b, c are positive integers such that a is a multiple of c.  => there exists some integer x…

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

A: False.

Q: Let A be the set of all positive integers whose last two digits form a number that is evenly…

A: We have the given condition as   Let us consider A be the set of all positive integers whose last…

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: 2. When the expression (156)(205) (557) is evaluated, it ends with a string of consecutive zero's.…

A:

Q: pls help asap!!!

A: According to guidelines we solve first three subparts when given multiple subparts.

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: O Determine whether M₁1 = 2¹¹ – 1 is prime by checking primes less than √M₁.

A: