(5) Show that if n ɛ Z+ is odd which is divisible by k distinct primes, then the congruence x2 = 1 (mod n) has 2* distinct solutions in Z/nZ.

Q: How many even 3-digit numbers can be formed from the digits 1, 3, 4, 8, and 9 with no repetitions…

A: Out of the total 5 digits 1, 3, 4, 8 and 9 given, the even digits are 4 and 8. For the 3- digit…

Q: factors of 24 that add up to 10

A: factors of 24 that add up to 10

Q: 4 2 G F -8 -4 -2 2 10 -2 -4 E 10 K 00

A: Formula for area is length multiply by breadth. Similarly for square its a^2 if side of square is…

Q: How many ordered triples of letters are there taken from the letters A, T, C, and G?

A: given letters: A,T,C and Gtotal number of letters = 4

Q: 4 Evaluate -1 0 5 by: 3 - 2 expanding along the first row expanding along the second column A A 1.…

A:

Q: Find L{1}ℒ{1}.

A:

Q: 4. Determine (16-912) dt c4

A: We will solve the problem.

Q: 6/4 - 2/4

A: Explanation and solutions is given below.....

Q: 7 items chosen 5 at a time

A:

Q: n?_4

A:

Q: Prove that the number of partitions of n into at most k parts is equal to that of partitions of n +…

A: given , number of partitions of n into k parts  we have to prove that , partitions of number n + k…

Q: 16 2/5- 8 4/9

A:

Q: 20/5+5+2*8

A: Consider the given expression

Q: Reduce the following to the lowest terms. Show how to calculate the greatest common divisor by the…

A: The given fraction number is,Here we can write,As we can see the number 4 can be canceled out.This…

Q: Randomly drawing and immediately three red M&Ms in a row from a bag that contains 10 red M&Ms out of…

A: Given: 30 total M&Ms in that 10 red M&Ms.

Q: factors of 20 that add up to 9

A:

Q: coefficient of variaton for given populaion   5,8,9,11,15,16,17,19

A:

Q: 1/4 +5/4

A: Solution: The objective is to find the value of the given expression

Q: 42. The term that does not contain x in the expansion of 8x +

A:

Q: 5 7/12 + 1 3/4 + 4 1/2

A: Given that 5712+134+412Solution  :5712+134+412=57+39+24612

Q: 1) (8s° - 9s) - (3s° + 4)

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

Q: 1/5 + 1/10 + 1/15

A: Sum of numbers

Q: 9 5/12 - 3 2/3 =

A: Case 1: Let the given number be in mixed fraction notation.

Q: 6 3/20 - 6 3/8

A:

Q: W 4. What is the value of the 4th term of the expansion (a + b)"? O a5 O 5a*b O 10a²63 10a b?

A:

Q: | (16 – 2*) dz =

A: To find : the value of ∫0216-x4dx   Using the formula ∫abxndx=1n+1bn+1-an+1

Q: Evaluabe: 25+3 se

A: Here we find Laplace inverse transform

Q: 5. Find the coefficient of a¹¹b4 in the expansion of (a + b)¹5.

A:

Q: Compute the indicated product.   -1 3   9 2 0   3 9 3

A:

Q: 5 2/5+ n= 75/6

A: Given query is to find the value of n.

Q: 6（c)(d)

A: We shall use the properties of homomorphism to solve this question

Q: 1. Use expansion along the 3rd row -4 3 1 2 -1 1 7 5

A: