for all integers a and b, a² + b² = 0, 1, 2, 4 or 5 modulo 8. Deduce that there do not a and b such that a² + b² = 12345790.

Q: .3x = 4(mod5).

A: From the given expression of the modulus, we will have to find out the value of X. This is…

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

A:

Q: For any real number a, a ≠ 0, show that a+4 a+7 a+5 a +8 = 0, a+6 а+9 a+1 a+2 a+3 and 4a7a 5a 8a =…

A: We are required to prove: a+1a+4a+7a+2a+5a+8a+3a+6a+9=0a4a7a2a5a8a3a6a9a=0aa4a7a2a5a8a3a6a9=0

Q: Express each nonnegative integer a less than 15 as a pair (a mod 3, a mod 5).

A: The values of a could be, 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14.

Q: The notation x = y mod n is used to indicate the unique integer x in the range 0 :$ x < n such…

A: Given statement is that the notation x = y mod n is used to indicate the unique integer x in the…

Q: a) Find integers a and b such that a + b =a-b (mod 5).

A:

Q: Give a definition of an inverse of a number a modulo m.

A: if the two integer a and m modulo then  let x is an integer value so the x is inverse of an only if…

Q: Find a positive integer less than 6 for x that sat 2x + 340 = 1703 (mod 5).

A:

Q: Find all four solutions to x2 =6 (mod 19 x×23) with 1<x< 437.

A: Solution:-

Q: If p times tne pth term of an A.P. is equal to q times the qth term of the same AP., then how that…

A: Given that If p times the pth term of an A. P. is equal to q times the qth term of same A. P.  To…

Q: Find all solutions in {0, 1,2, ..., 12} to x26 + 15x13 = 12 mod 13.

A:

Q: True or false? If f and g are increasing interval I, then fat is on an increasing on I

A:

Q: Suppose Cov(X,Y) = 725. What is Cov(0.72X, 0.62Y)?

A: The objective of this question is to find the covariance of the two variables 0.72X and 0.62Y given…

Q: Find 8081 mod 11.

A:

Q: 137 mod |

A: The answer is : 7137 (mod 11) = 6  The detailed solution is as follows below:

Q: Evaluate |1 – cos40 de O 1/(2v2) V2/2 O None of the choices O 1/2

A:

Q: Compute (3714 - 39) mod 9 without a calculator.

A:

Q: SorvE THモ CONGROEモNしE 626 X Rエ mod5

A: As 5 is an odd number, by fermat's theorem, we have             x5-1 = 1 (mod 5)           =&gt; x4…

Q: Show that if a ≡ b (mod m) and c ≡ d (mod m), then a + c ≡ b + d (mod m).

A:

Q: 2 2 Let A = Compute 412 - A and (412)A. 6-2

A:

Q: Find the solutions of the congruence 15x2 + 19x ≡ 5 (mod 65)

A: The given equation is: 15x2+19x≡5(mod 65)

Q: x² - 2x = 8(mod19) X= (mod19)

A:

Q: Let a and b be relatively prime positive integers. Show that a(b) + b(a) = 1(mod ab).

A: Solution:

Q: let a, b, and m be integer, prove that if 2a+3b>=12m+1, than a>=3m+1, or b>=2m+1

A: To prove: For integer a, b, and m if   2a+3b≥12m+1Than, either a≥3m+1, or b≥2m+1.

Q: Let c, a, ß be nonzero real numbers such that c + B. Find a given that 00 162n-3 ac² cn 4

A:

Q: If a mod b = 0, then b | a true or false

A: It's  pronounced “a is congruent to b mod n” (or “a is congruent to b modulo n”). Basically, it…

Q: Suppose that a and b are integers with a = 11(mod 19) and b = 3(mod 19). Find the integer c such…

A:

Q: Find a number a such that 70a = 1 mod 17.

A:

Q: For each pair of integers m and d, calculate m mod d. Show your work! a. m = 43 and d = 9 b. m 50…

A: If m and d be two integers . Then m mod d means that the remainder when m is divided by d .

Q: For any integer a, prove that a = 0 or 1 (mod 3).

A:

Q: Find the remainder of 5130 modulo 28

A: Chinese Remainder Theorem : Let n1​,n2​,n3​,...,nk​∈N , with GCD(ni​,nj​)=1 for each i=j. Let…

Q: 5x² + 3x = 3(mod17) X = (mod17)

A: Given that 5x2+3x≡3 (mod 17)x(5x+3)≡3 (mod 17)x≡3 (mod 17)  or   (5x+3)≡3 (mod 17)x≡3 (mod 17)  or…

Q: Find all inverses of 7 modulo 37.

A:

Q: Suppose that a, b are integers such that 1 = -19a + 45b. Use this information to find all integers a…

A: The given equation 1=−19a+45b suggests that 1 is a linear comb.−19 and 45 with coefficients a and…