Mathematics Homework Solutions

Euler Totient Function

For this problem it helps to know that: 3x7x13 = 273 (a) Define the Euler Totient function, (SYMBOL) For (b) to (f) please see attached. (PLEASE SEE ATTACHMENT FOR COMPLETE PROBLEM AND PROPER SYMBOLS)

Posting ID: 27707

Odd Prime; Inverse; Lemma; Wilson's Theorem

Assume p is an odd prime ... *See attachment for questions

Posting ID: 27708

Proof about congruence modulo 43 (also expressible as equivalence modulo 43)

Let S = Z_43 (where the underscore, "_", indicates that what follows it, in this case 43, is a subscript). Let Q be a subset of S that contains ten non-zero numbers (i.e., that Q contains ten non-zero elements of S). Prove that Q contains four distinct numbers "a," "b," "c," "d" such that ab = cd in Z_43.

Posting ID: 27709

Context Free Grammars

Following is a big-oh relationship. Give witnesses n0 and c that can be used to prove the relationship. Choose your witnesses to be minimal, in the sense that n0 - 1 and c are not witnesses, and if d < c, then n0 and d are not witnesses. n¹º is O(3ⁿ)

Posting ID: 27730

Context Free Grammars / Languages from Grammars

On the ith round {see attached}, what is the length of the shortest string that is new for either of the syntactic categories? What is the length of the longest new string for: a) b)

Posting ID: 27741

Context Free Grammars / Productions

Write productions that will define the syntactic category , to replace the abstract terminal simpleStat in the figure below {see attachment}. You may assume the syntactic category stands for C arithmetic expressions. Recall that a "simple statement" can be an assignment, function call, or jump, and that ...continues

Posting ID: 27780

Nonnegative Integers

Please see the attachment for problem related to nonnegative integer and my solution (needs to be edited and confirmed)

Posting ID: 27790

Nonnegative Integers

If the solution to this nonnegative integer question is correct, then you may respond that it is. If the solution needs ANY kind of improvement, in presentation, in clarity, in correctness, if a proof can be more elegant, then please rewrite the entire solution.

Posting ID: 27879

Only Respond if you are OTAs: 101478, 103846, 104591, 104455

Respond/pick up the credit if you absolutely know the solution is correct. If you can make an improvement on the solution in correctness, clarity, presentation, or if a proof can be more elegant, than please rewrite the entire solution.

Posting ID: 27882

Prove that in any graph...

Prove that in any graph with two or more vertices, there must be two vertices of the same degree.

Posting ID: 28046
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