Please answer the following two questions.
Please answer the following two questions. Find the smallest positive integer solution to the equation. Show...
(1 point) Find the smallest positive integer solution to the following system of congruence: x = 5 (mod 19) = 2 (mod 5) = 7 (mod 11) x =
Find the smallest positive solution and the general solution to the system x ≡ 1 (mod 3), x ≡ 2 (mod 5) and x ≡ 3 (mod 7). Exercise 2 (5 points Find the smallest positive solution and the general solution to the system ΧΞ2 (mod 5) and r Ξ 3 (mod 7). 1 (mod 3),
8-7. Find the smallest positive integer a such that 5:13 +13n" + a(9) = 0 (mod 65) for all integers n.
let m=(82! /21). find the smallest positive integer x such that m≡x(mod 83)
Please show steps with explanations 3. Find the smallest positive integer k such that 1222+32++ n2 is big-O of nk. Explain.
What is the smallest positive integer n that has the following characteristics? n mod 3=2,n mod 5=3, and n mod 7=5
Please write neatly and clearly, show all work. Thank you! (I've been stumped for awhile) (1 point) Find the smallest positive integer x that solves the congruence: 11x = 4 (mod 68) x = (Hint: From running the Euclidean algorithm forwards and backwards we get 1 = s(11) + +(68). Find s and use it to solve the congruence.)
please answer questions #7-13 7. Use a direct proof to show every odd integer is the difference of two squares. [Hint: Find the difference of squares ofk+1 and k where k is a positive integer. Prove or disprove that the products of two irrational numbers is irrational. Use proof by contraposition to show that ifx ty 22 where x and y are real numbers then x 21ory 21 8. 9. 10. Prove that if n is an integer and 3n...
Could you please help me on these 5 questions? Thank you! Find the exact value of the following expression in degrees without using a calculator or table. -19 -190 We were unable to transcribe this imageFind all angles (in degrees) that satisfy the following equation. sin a = 1 Select the correct choice below and, if necessary, fill in the answer boxes to com 1}. where k is any integer. O A. The solution set is {a la = °...
Modern Algebra, MAT 401 Test 3. Show your work (b) 1. Find a solution x E ZOSXsn for the congruence (a) 8x+3= 5 mod 9 8x=l(mod 21) 2. Find the least positive integer that is congruent to: (a) (14+46+65+92Xmod 11) (b) (717)(32)(62)(mods) (c) 62(mod5) 3. Solve the system (a) x = 2(mod 5) em a lx = 3(mod 8) x 4(mod 7) (3x + 2 = 3(mod 8) 4. Solve the system (a) [4][x] + [2][y] = [1] () {[3][x]...