Prove that there are no solutions in positive integers to equation x^4 + y^4 = 100

Prove that there are no solutions in positive integers to equation x^4 + y^4 = 100

Discrete Structures

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Discrete Math

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Counting methods and proofs

Discrete Structures - How many strings of eight letters (from A, B, C, ... Z) are there.... Please see attached file. thank you.

Counting strings

How many bitstrings of length 10 are there that contain 5(or more) consecutive 0’s or contain 5(or more) consecutive 1’s? Justify your answer.

Finite proof

Let R ba a partial order on S, and suppose that x is a unique minimal element in S. a) prove that S is finite, then xRy for all s in S b) show that the conclusion in (a) need not be true if S is infinite

Relations and sets

1) Find a relation R on a set S that is neither Symmetric nor antisymmetric 2) Let S be a set containing exactly n elements. How many antisymmetric relations on S are there. 3) give a recursive definition of X^n for any positive integer n 4) give a recursive definition of the nth odd positive integer 5) Let g: Z -> Z ...continues

Recurrence Relations

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Boolean expression

Please see attached file Write the Boolean expression associated with each circuit.

Discrete structures in mathematics and computer science

Q1) Use the standard logical equivalences to simplify the expression (ㄱp ^ q) v ㄱ(pVq) Q2) consider the following theorem "The square of every odd natural number is again an odd number" What is the hypothesis of the theorem? what is the conclusion? give a direct proof of the theorem. Q3) consider the follo ...continues