20. 79x = 83 (mod 61)

Q: Find a positive integer less than 8 for x that satisfies x = 720 + 3 (mod 7).

A:

Q: Odd numbers between 16 and 80 that are multiples of 7.

A: Odd Numbers: An odd number is an integer that is not divisible by 2. Example, 3, 5, 7 etc. Multiple:…

Q: Least residue of 8^68 modulo 17

A:

Q: Q: Find the remainder of 2^ 2019 when divided by (a) 2. (b) 5. (c) 7. (d) 9

A: We have to find the remainder when 22019 is divided by: (a) 2 (b) 5 (c) 7 (d) 9

Q: Solve y² = 37(mod 77)

A: We have to find the value of y  Using quadratic reciprocity property we find value of y

Q: 10. (8 points) Solve 3x 2, (mod 7) or show that no solution exists.

A: Solution: The objective is to find the solutions of 3x≡2 (mod 7)

Q: If a = 17 (mod 3), then what is the remainder of a when divided by 3? Enter the numerical value.

A:

Q: Please find x

A: To solve the congruence x173≡428(mod541), we can follow these steps:1. Check if 541 is prime: First,…

Q: In this exercise set, all variables are integers. 1. List the distinct congruence classes modulo 5,…

A: We can solve this using linear congruence method

Q: Compute 21200 mod 27.

A: We want to compute 21200 mod 27.

Q: Find 110 + 220 + 330 + 440 + 550 + 660 (mod 7)

A: 110+220+330+440+550+660mod 7 We need to find the value of above expression.

Q: Find all solutions for x, up to congruence.  x ≡ 3^2017 (mod 100)

A: Given Data: To find the value of x.  x ≡ 3^2017 (mod 100)