Question

find whether x^n + y^n is divisible by x-y (y≠0) or not.​

Answer 1

Answer:

Step-by-step explanation:

Definition of integer:

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

Definition of natural number:

All positive integers from 1 to infinity that are considered natural numbers are included in the number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.

The numbers that are used for counting and are a subset of real numbers are known as natural numbers. The only positive integers in the set of natural numbers are 1, 2, 3, 4, 5, 6 . . . . .

find whether x^n + y^n is divisible by x-y (y≠0) or not.​

No

Let P(n) be the statement that, for any integers x and y, $x^ n-y^ n$is divisible by x-y. Consequently, P(l): x1 - y1 = x-y is divisible by (x-y) P(l) is therefore true. Assume for the moment that n = k is a natural integer and P(n) is true. P(k) states that$x^ k-y^ k$ is divisible by (x - y). So long as P(k) is true, P(k + 1) is also true. P(n) is true for any natural number n according to the principle of mathematical induction.  

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Answer 2

Answer:

Answer:

Step-by-step explanation:

Definition of integer:

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

Definition of natural number:

All positive integers from 1 to infinity that are considered natural numbers are included in the number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.

The numbers that are used for counting and are a subset of real numbers are known as natural numbers. The only positive integers in the set of natural numbers are 1, 2, 3, 4, 5, 6 . . . . .

find whether x^n + y^n is divisible by x-y (y≠0) or not.

No

Let P(n) be the statement that, for any integers x and y,

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is divisible by x-y. Consequently, P(l): x1 - y1 = x-y is divisible by (x-y) P(l) is therefore true. Assume for the moment that n = k is a natural integer and P(n) is true. P(k) states that

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is divisible by (x - y). So long as P(k) is true, P(k + 1) is also true. P(n) is true for any natural number n according to the principle of mathematical induction