Which numbers from the set{-63,-54, -41, 11, 13, 76, 80, 130, 132, 137} are congruent to 7 mod 13? 137 13, 130 -63, 80, 132 -54, -41, 11, 76

Q: Is a set {-22,-3,0,1,5,9,10} modulo 7 a RRS? Why? Is a set {-5,-22,-15,-9,-2,5,8,10,25,34,48} modulo…

A: A subset S of the integers is called a reduced residue system modulo n if: gcd(r, n) = 1 for each r…

Q: How many different three digit numbers can be made from the set of integers {1,2,3,4,5,6,7,8,9} if…

A: The set of integers {1,2,3,4,5,6,7,8,9}

Q: How many permutations of the numbers (1, 2, 3, 4, 5, 6, 7, 8, 9} have the numbers 4, 5 and 6 in…

A: So, the numbers 4, 5 & 6 should remain at their natural position and the other numbers can…

Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

A:

Q: Prove that an odd number multiplied by an odd number is odd.

A: The objective is to prove that an odd number multiplied by an odd number is odd.

Q: How many numbers between 1 and 10000 have the digits 1,3, and 5 such that each digit appears exactly…

A: Here Numbers between 1 and 10,000 have digits 1,3,5 and each appears exactly once only

Q: 2

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 any prime number Divide ‘p’ by 6, we get P=6q+r       - (1);     r=1,2,3,4,5 And q be any…

Q: Using the set {1,3,4,6,7,8,9}, how many odd numbers can we construct between 100-999 if no element…

A: An odd number is determined by the unit digit. If the unit digit is an odd number, then the number…

Q: Show that given any set of 5 natural numbers, there are 3 numbers whose sum is divisible by 3.

A: Let q∈N. Note that, for every q there exists some x∈N and some v∈0,1,2 such that q=3x+v. Now, let…

Q: How many integers in the set {1,2,3,4, ..., 200} is divisible by at least one of the primes 2, 5 and…

A: Just use inclusion-exclusion principle for three sets.

Q: show that every integer greater than 11 is the sum of two composite integers

A: We need to prove that  every integer greater than 11 is the sum of two composite integers.

Q: Evaluate  1/2 + 1/4 + 1/8 + 1/16 + ... + 1/1024

A:

Q: Assume that all four-digit integers (numbers from and including 1000 to and including 9999) are…

A:

Q: How many three digit numbers (values between 100 and 999 inclusive) are divisible by four? How many…

A:

Q: How many integers from 1 to 99,999 contain exactly two consecutive 1s?

A:

Q: How many 3-digit numbers can be formed from the prime numbers from 0 to 10 if the repetition of the…

A: We need to find how many 3 - digit numbers can be formed from the prime numbers from  0  to  10  if…

Q: How many six-number combinations can be generated from the numbers from 1 to 42 inclusive, without…

A: Given information: A 6 number combination is to be generated. The possible numbers are selected…