10. Define in the language of arithmetic: (a) x and y are relatively prime; (b) x is the smallest...
IfX= 4, and Y - 6, the arithmetic (simple) average of X and Y is: a 10 oo QUESTION 8 Given Y - 2X, when X= 3, then Yis equal to: 3 5 2/3 312 QUESTION 9 If X is greater than Y, then-X is less than-Y True False QUESTION 10 If X is greater than Y, then (1/%) is greater than (17). True False
2. Prove that a(x) and b(x) are relatively prime if and only if there exist polynomials f(x) and g(x) in F[x] such that f(x)a(x) + g(x)6(x) = 1.
Language C to find the greatest and smallest among 4 numbers. Use else if. Sample Output: Enter four numbers: 2 10 -9 Greatest is 10 and smallest is -9
Let P, Q ∈ Z[x]. Prove that P and Q are relatively prime in Q[x] if and only if the ideal (P, Q) of Z[x] generated by P and Q contains a non-zero integer (i.e. Z ∩ (P, Q) ̸= {0}). Here (P, Q) is the smallest ideal of Z[x] containing P and Q, (P, Q) := {αP + βQ|α, β ∈ Z[x]}. (iii) For which primes p and which integers n ≥ 1 is the polynomial xn − p...
15. If (A, X, B) is an arithmetic sequence and (A, Y, B) is a geometric sequence so that A and B are positive and A #B, then ... A. Y = X B. Y < X C. Y >X D. XY = 1
Let L be a recursive language. Define L' = {x : there is y such that yxy belongs to L. Show that L' is r.e.
4.1 6b Let A be the set {a,b,c}, and define a relation on A as R = {(x,y) E AXA : 2x + y is prime}. Prove that R is a function with domain A.
#define minl (x, y) ( (x < y) ? x : y) #define min 10 #include <stdio.h> int min2(int x, int y) { if (x < y) return x; else return y; } main() { int a, b; scanf("%d %d", &a, &b); if (b < min) printf("input out of range\n"); else { a = minl(a, b++); printf("a = %d, b %d\n", a, b); a = min2(a, b++); printf("a = %d, b %d\n", a, b); } } ------------------------- 1 Give the...
C1= 5 C2= 6 C3= 10 GCD --> Greater Common Divisor B1 a. Let x := 3C1 + 1 and let y := 5C2 + 1. Use the Euclidean algorithm to determine the GCD (x, y), and we denote this integer by g. b. Reverse the steps in this algorithm to find integers a and b with ax + by = g. c. Use this to find the inverse of x modulo y. If the inverse doesn't exist why not?...
c and 21 Let a, b, c E Z, where a and b are relatively prime nonzero integers. Prove that if a blc, then abc.