(a) How many solutions does the equation 3. x2 (mod 2017) 7 have in Z2o1r? (Note that 2017 is a prime mumbern (a) How many solutions does the equation 3. x2 (mod 2017) 7 have in Z2o1r? (Note...
How many classes of solutions are there for each of the following congruences? (a) x2 - 1 = 0 mod (168) (b) x2 + 1 = 0 mod (70) (c) x2 + x + 1 = 0 mod (91) (d) x3 + 1 = 0 mod (140) Please note to show how you got the solutions as well as finding out how many classes of solutions there are for each congruence. Please explain every step so I can understand how...
Let p be a prime. Show that Zp(X)/(X2+1) is a field iff the equation x2=-1 has no solution (mod p).
Please explain the conception and follow the comment How many possible solutions exists for the equation x1 + x2 + x3 = 7 when x1; x2; x3 are non-negative integers (i.e. x1; x2; x3 2 f0; 1; 2; 3; :::g).
Let a,b, and c be prime numbers that are each odd and distinct from each other. How many solutions does the congruence = 1 mod abc have?
)Consider the non-negative integer solutions to x1 + x2+ x3 + x4 + x5 = 2020. (A) How many solutions does Equation (1) have satisfying 0 ≤ x1 ≤ 100? Explain. (B) Remember to explain your work. How many solutions does Equation (1) have satisfying 0 ≤x1 ≤ 100, 1 ≤x2 ≤ 150, 10 ≤x3 ≤ 220?
Which of the following equations have solution? justify your answers a) x2 =3 (mod 137 ) this mean x to the 2nd power congruence to 3 mod 13 to the 7 power b) x3 =4 (mod 115.239) this mean x to 3rd power congruence to 4 mod 11 to the 5 th power times 23 to the 9th power c) x7=2(mod49) this mean x to the 7th power congruence to 2 mod 7 to the 2nd power d) x7 =...
I need help with number 3 on my number theory hw. Exercise 1. Figure out how many solutions x2 = x (mod n) has for n = 5,6,7, and then compute how many solutions there are modulo 210. Exercise 2. (a) Find all solutions to x2 +8 = 0 (mod 11). (b) Using your answer to part (a) and Hensel's Lemma, find all solutions to x2 +8 = 0 (mod 121). Exercise 3. Solve f(x) = x3 – x2 +...
Can someone solve these for me? Consider the equation X1 X2X3 + X4+X5 40. How many different solutions does this equation have if all the variables must be positive integers? Enter the exact numeric answer QUESTION 2 Suppose that a license plate consists of three letters followed by three digits. How many different license plates start with the letter A if letters and digits cannot be repeated? Enter the exact numeric answer. Consider the equation X1 X2X3 + X4+X5 40....
Question A: Logarithmic Equations A1. (x 1)2 2. How many real solutions does it have? Solve the equation logz(x
76.Let p be an odd prime. Prove that if Ord, (a) = his even, then a/2 = -1 mod p. 77.let p be an odd prime. Prove that if Ord, (a) = 3, then 1+ a + a? = 0 mod p and Ord,(1 + a) = 6. 78.Show that 3 is a primitive root modulo 17. How many primitive roots does 17 have? Find them.