Question

Show that if m×n=1 then m=n=1 or m=n=-1

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Hermann

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Given that m \times n = 1 , we want to show that m = n = 1 or m = n = -1 .

Let's assume thatm and n are integers.

Ifm = 1 and n = 1 , then m \times n = 1 \times 1 = 1 , which satisfies the given condition.

Ifm = -1 and n = -1 , then (-1) \times (-1) = 1 , which also satisfies the given condition.

Let's consider the case wherem and n are not both equal to 1 or both equal to -1.

Assume without loss of generality thatm = 1 and n = -1 . Then we have m \times n = 1 \times (-1) = -1 \neq 1 .

Therefore, the only solutions form \times n = 1 are m = n = 1 or m = n = -1 .

\textbf{Answer:}m = n = 1 or m = n = -1

Let's assume that

If

If

Let's consider the case where

Assume without loss of generality that

Therefore, the only solutions for

\textbf{Answer:}

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