Question Consider the poset given by ({1,2, 3.4. 6. 8.24}, |). Is the poset a la

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Consider the poset given by ({1,2, 3.4. 6. 8.24}, |). Is the poset a lattice? Explain. Draw the Hasse diagram for the poset. Given that a and x are integers, a > 1; a|(3x + 2) and a|(12x + 3). find a. Suppose a and b are relatively prime integers and c is an integer such that a | c and b c. Prove that ab | c . [Hint: you will need to use the definitions of "relatively prime" and "divides"] Use the Euclidean Algorithm to find the greatest common divisor of a = 1047 and b = 259 and express it in the form ma + nb for suitable integers m and n. Define f: N {1} rightarrow N by setting f (n) equal to the largest prime divisor of n. Find the range of f. is f one-to-one? is f onto? Why did we not express f as a function N rightarrow N ? Explain your answers. This question concerns congruence mod 11. List 4 positive and 2 negative integers in 4bar and in -4bar. What is the general form of an integer in 4bar and of an integer in -4bar? Find 242 (mod 15). List all congruence classes for congruence mod 6, giving the most usual and one other name for each. Use Fermat's Little Theorem to compute 3502 (mod 503), 3503 (mod 503) and 3505 (mod 503).

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