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Question

Direction (Q. Nos. 3-6) : Read the following passage and answer the questions that follow. Your answers to these questions should be based on the passage only :

Passage
Despite how closely the problem is related to the Pythagorean theorem, which has infinite solutions and hundreds of proofs, Fermat's subtle variation is much more difficult to prove. The 17th-century mathematician Pierre de Fermat wrote in 1637 in his copy of Claude Gaspar Bachet's translation of the famous Arithmetica of Diophantus : "I have a truly marvellous proof of this proposition which this margin is too narrow to contain." However, no correct proof was found for 357 years, until it was finally proven using very deep methods by Andrew Wiles in 1995 (after a failed attempt a year before). All the other theorems proposed by Fermat before and after this were eventually proven or disproven, either in his own proofs or by other mathematicians, in the two centuries following their proposition. The theorem was not the last that Fermat conjectured, but the last to be proven.

Which of the following best describes the timeline of Fermat's Last Theorem compared to his other conjectures?

The correct answer is

It was neither the first nor the last he proposed, but it was the final one to be resolved

Fermat's Last Theorem: Timeline of Resolution

Fermat's Last Theorem, which states that the equation $x^n + y^n = z^n$ has no positive integer solutions for $n > 2$, was a conjecture proposed by Pierre de Fermat around 1637.

Context Among Fermat's Conjectures

  • Pierre de Fermat was known for proposing many mathematical statements and problems.
  • Fermat's Last Theorem was neither the first nor the last conjecture he put forward during his extensive work.

Resolution Status

Although proposed relatively early among his conjectures, Fermat's Last Theorem became one of the most famous and enduring unsolved problems in mathematics for over 350 years.

Crucially, it was the final major conjecture proposed by Fermat to be successfully resolved mathematically. The proof was finally completed by Andrew Wiles in 1994-1995.

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Important Questions from Reading Comprehension

  1. Why, according to the writer can't people be motivated to use a resource prudently?

    1. They feel that others may overuse the resource

    2. It is possible to substitute the resource

    3. Abundance of the resource availability

    Select the correct answer using the code given below:

  2. When do people use resources exhaustively?

  3. The self-interest of people affects the use of renewable resources

  4. People rooted in a locality

  5. Which among the following is closest in meaning with the word 'deplete'?

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