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Pairs of numbers are relatively prime

Assignment Help Basic Computer Science
Reference no: EM132290108

1) Show that P is closed under union, concatenation, and complement.

2) Let CONNECTED = {?G?| G is a connected undirected graph}. Analyze the algorithm given on page 185 to show that this language is in P.

3) A triangle in an undirected graph is a 3-clique. Show that TRIANGLE ∈ P, where

TRIANGLE = {?G?| G contains a triangle}.

4) Let

MODEXP = {?a, b, c, p?| a, b, c, and p are positive binary integers

such that ab ≡ c (mod p)}.

Show that MODEXP ∈ P. (Note that the most obvious algorithm doesn't run in polynomial time. Hint: Try it first where b is a power of 2.)

5) Which of the following pairs of numbers are relatively prime? Show the calculations that led to your conclusions.

a. 1274 and 10505

b. 7289 and 8029

Reference no: EM132290108

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