Take p and q are primes and p=3mod4 and q=3mod4. Take n=pq such that an integer z has a square root d mod n such that d^2=z modn. Explain why z also has a squar root mod p and mod q.

Q: b"=1 (mod n) is valid for which of the following pair (b,n) (9.7,1729) (97,1729) (-97,1729)…

A: Answer

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

A:

Q: If a = b (mod m) and a = b (mod n) then a = b (mod mn)

A:

Q: b=3(mod19)

A:

Q: 7x = 4 (mod 12).

A:

Q: 4x=22(mod10)

A:

Q: 3x = 1 (mod 6)

A: 3x≡1 (mod 6) ⇒ 3x-1≡0 (mod 6)This means 3x-1 is divisible by 6.

Q: 37x = 101 (mod 151)

A:

Q: Show that 127 = -16(mod 13) and show that 300 = 1(mod 13).

A:

Q: What is the largest value that m mod n can be?

A: Largest value of m mod n is n-1.

Q: Find the value of 786 (mod 13) using Fermat's Little Theorem. Remember, x (P - 1) = 1 (mod p) 786 =…

A:

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

A:

Q: Find 1112 mod 13.

A:

Q: Identify if the given statement is true or false: I. If a is an integer, the (a^2 is congruent to 0…

A: Given some statements. Check whether these statements are true or false.

Q: Find  mod (40, 7) and div (40, 7).   mod(40, 7)=? div(40, 7)=?

A: 1) mod(40,7)  is the remainder when 40 is divided by 7we know that 7×5 =35  and 7×6=42as 7×6=42 is…

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

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

Q: Find  mod (59, 10) and div (59, 10).

A:

Q: 17!=1(mod19). Select one: True False

A:

Q: Show that y = x (mod p) leads to -y = -x (mod p).

A:

Q: Find the order of 4 modulo 49.

A: Evaluate order of 4 modulo 49.

Q: there are 3 square roots of 0 when we work mod 45 give all 3 of them

A:

Q: Find 123 (mod 11) + 321 (mod11).

A:

Q: Compute the following modular exponents. 11^6mod14=   11^ 5 mod 15 =. 3^3mod5 =

A:

Q: 5^14 ( mod 26).

A:

Q: ere they want me to find a div m and a mod m when a = −33, m = 67. How I solved, I divided -33 into…

A: To find a div m and a mod m when a = −33, m = 67. Given information:  a = -33 m = 67

Q: Show that if x mod 8 = 1, then (3x −5) mod 6 = 4.

A: Solution

Q: Q2/let n be a fixed positive integer and a,b be arbitrary integers. Then a = b (modn) iffa and b…

A: We have to prove that Given statement

Q: Use Fermat’s little theorem to find 7121 mod 13.

A:

Q: Fermat's Little Theorem tells us that if p is prime and a is an integer not divisible by p, then…

A:

Q: What is the smallest positive integer x in the equarion: 1=3x+2(mod 7)?

A: We have to solve the equation 1 = 3x + 2 (mod 7)⇒1 - 2 - 3x = 0 (mod 7)⇒-1 - 3x = 0 (mod 7)⇒3x = - 1…

Q: Figure out how many solutions x² = x(mod n) has for n = 5,6,7 and then compute how many solutions…

A: