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

Q: if a equiv b (mod n) , then a⁴ equiv b⁴ (mod n) for any positive integer 4.

A:

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: If x^677 ≡ 3 mod 2020, find x.

A: We have   x677≡3mod2020⇒x677-3=2020m   where m is integer different values of m we get different…

Q: Is 1501 square modulo of 3738

A: Explanation:To determine if 1501 is a square modulo 3738, we need to find an integer x such that…

Q: Find the smallest distinct postive numbers that provide a counterexample to show the statement is…

A: Let the odd numbers be 1 and 3 and the even number be 2, According to the question, The sum of any…

Q: If a and b are positive integers, which of the following can never be the gcd(56a, 63b)? (а) 56а (b)…

A: given a and b are positive integers,  and to find gcd(56a, 63b) gcd of (56, 63) is 7  so gcd(56a,…

Q: + 220 + 330 + 440 + 550 + 660 (

A:

Q: 37x = 101 (mod 151)

A:

Q: Determine the least residue of 56^1010 (mod 323).

A:

Q: Find 8081 mod 11.

A:

Q: 12 = -3 (mod 5) Select one: True False

A:

Q: Find the least residue of  -5 -46 modulo 14.

A:

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

A:

Q: Find all solutions for x, up to congruence 7^78 (mod 79)

A:

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

A:

Q: Find 1112 mod 13.

A:

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: 1. Prove that f1 + f²+...+ ƒ/²/2 = ƒnƒn+1, where n is a positive integer and fn is the nth Fibonacci…

A: The Fibonacci numbers are the numbers in the following integer sequence.…

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

A: False.

Q: Solve for X, show all calculation in binary number system only X = ((1110)₂-(0011)₂) (10011010)₂)…

A:

Q: 21. How many positive integers x are there such that 3x has 3 digits and 4x has four digits?

A:

Q: x² + x = 13(mod17) X= * (mod17)

A:

Q: Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5

A:

Q: S(x + Vx)dx 73 6.

A:

Q: Calculate 2^1212 (mod 9211), reducing it to a positive number less than 9211. Show your…

A: We have to find out remainder when Noted that Since So to get the required result ,we have to find…

Q: Find the integer that satisfies: 30x4 ≡ 12 (mod 67)

A: Given the expression is, 30x4≡12mod 67

Q: Find all integer values of x for which 3x = 4 (mod 8).

A: given congruence equation 3x≡4(mod 8)

Q: Show that 18! ≡ -1 (mod 437).

A: We have to show that: 18!≡-1mod437

Q: TRUE or FALSE: 1. There is no integer n such that 4 | (n^2-2) 2. The GCD of all prime numbers is 1.…

A:

Q: Prove that a1 + a2 = b₁ + b₂ mod n.

A: We have to prove that a1+a2=b1+b2 (mod n).Given:a1≡b1 (mod n)a2≡b2 (mod n)This means there exist…

Q: Find the order of 4 modulo 49.

A: Evaluate order of 4 modulo 49.

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

A:

Q: show that no integer of the form n^3+1 is a prime other than 2

A:

Q: If a and b are positive integers, which of the following can never be the gcd(56a, 64b)? (а) 56а (b)…

A:

Q: 6. In an efficient way verify that the number 1 is the only positive integer number that…

A:

Q: Find all integers sx such that 2x = 5 (mod 7).

A:

Q: Which of the following is an Integer ?

A: Given,           Ingeger number.

Q: Show by using construction that n^2+5n+6 is not prime for any n is a natural number.

A:

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: What is the set of O of odd positive integers less than 10?

A: The odd positive integers less than 10 are 1, 3, 5, 7, 9.