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.

According to the passage, why did Pierre de Fermat not provide the proof for his proposition in his copy of Arithmetica?

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?

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.

The passage draws a contrast between the Pythagorean theorem and Fermat's proposition. What is the primary basis of this contrast?