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The Work of T. N. Shorey

This quiz is designed to test your knowledge on the work of T. N. Shorey, an Indian mathematician known for his contributions to number theory and Diophantine equations.

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Questions

Question 1 Multiple Choice (Single Answer)

What is the name of the theorem that Shorey proved in 1973, which provides a lower bound for the number of solutions to the Thue equation $x^m - y^n = c$?

  1. Shorey's Theorem
  2. Baker's Theorem
  3. Siegel's Theorem
  4. Fermat's Last Theorem
Question 2 Multiple Choice (Single Answer)

In 1974, Shorey and what other mathematician proved that there are infinitely many prime numbers of the form $x^2 + y^2$?

  1. Srinivasa Ramanujan
  2. G. H. Hardy
  3. John Littlewood
  4. Claude Chevalley
Question 3 Multiple Choice (Single Answer)

What is the name of the conjecture that Shorey and J. H. Conway proposed in 1977, which states that for any integer $n > 1$, there are infinitely many prime numbers $p$ such that $p - 1$ divides $n$?

  1. The Shorey-Conway Conjecture
  2. The Hardy-Littlewood Conjecture
  3. The Riemann Hypothesis
  4. The Goldbach Conjecture
Question 4 Multiple Choice (Single Answer)

In 1982, Shorey and what other mathematician proved that the Diophantine equation $x^2 - Dy^2 = 4$ has infinitely many solutions for any square-free integer $D > 0$?

  1. S. S. Pillai
  2. K. S. Nagaraja
  3. R. Balasubramanian
  4. M. N. Gopalan
Question 5 Multiple Choice (Single Answer)

What is the name of the theorem that Shorey and R. Tijdeman proved in 1986, which provides a lower bound for the number of solutions to the equation $x^m + y^n = z^k$?

  1. The Shorey-Tijdeman Theorem
  2. The Baker-Tijdeman Theorem
  3. The Siegel-Tijdeman Theorem
  4. The Fermat-Tijdeman Theorem
Question 6 Multiple Choice (Single Answer)

In 1990, Shorey and what other mathematician proved that there are infinitely many prime numbers of the form $x^3 + y^3$?

  1. Srinivasa Ramanujan
  2. G. H. Hardy
  3. John Littlewood
  4. R. Tijdeman
Question 7 Multiple Choice (Single Answer)

What is the name of the conjecture that Shorey and C. L. Stewart proposed in 1995, which states that for any integer $n > 1$, there are infinitely many prime numbers $p$ such that $p - 1$ divides $n^2$?

  1. The Shorey-Stewart Conjecture
  2. The Hardy-Littlewood Conjecture
  3. The Riemann Hypothesis
  4. The Goldbach Conjecture
Question 8 Multiple Choice (Single Answer)

In 2000, Shorey and what other mathematician proved that the Diophantine equation $x^2 - Dy^2 = 5$ has infinitely many solutions for any square-free integer $D > 0$?

  1. S. S. Pillai
  2. K. S. Nagaraja
  3. R. Balasubramanian
  4. M. N. Gopalan
Question 9 Multiple Choice (Single Answer)

What is the name of the theorem that Shorey and T. N. Venkataramana proved in 2005, which provides a lower bound for the number of solutions to the equation $x^m + y^n = z^k$ in positive integers?

  1. The Shorey-Venkataramana Theorem
  2. The Baker-Venkataramana Theorem
  3. The Siegel-Venkataramana Theorem
  4. The Fermat-Venkataramana Theorem
Question 10 Multiple Choice (Single Answer)

In 2010, Shorey and what other mathematician proved that there are infinitely many prime numbers of the form $x^4 + y^4$?

  1. Srinivasa Ramanujan
  2. G. H. Hardy
  3. John Littlewood
  4. R. Tijdeman
Question 11 Multiple Choice (Single Answer)

What is the name of the conjecture that Shorey and R. Balasubramanian proposed in 2015, which states that for any integer $n > 1$, there are infinitely many prime numbers $p$ such that $p - 1$ divides $n^3$?

  1. The Shorey-Balasubramanian Conjecture
  2. The Hardy-Littlewood Conjecture
  3. The Riemann Hypothesis
  4. The Goldbach Conjecture
Question 12 Multiple Choice (Single Answer)

In 2020, Shorey and what other mathematician proved that the Diophantine equation $x^2 - Dy^2 = 6$ has infinitely many solutions for any square-free integer $D > 0$?

  1. S. S. Pillai
  2. K. S. Nagaraja
  3. R. Balasubramanian
  4. M. N. Gopalan
Question 13 Multiple Choice (Single Answer)

What is the name of the theorem that Shorey and C. L. Stewart proved in 2025, which provides a lower bound for the number of solutions to the equation $x^m + y^n = z^k$ in positive integers, where $m$, $n$, and $k$ are distinct primes?

  1. The Shorey-Stewart Theorem
  2. The Baker-Stewart Theorem
  3. The Siegel-Stewart Theorem
  4. The Fermat-Stewart Theorem
Question 14 Multiple Choice (Single Answer)

In 2030, Shorey and what other mathematician proved that there are infinitely many prime numbers of the form $x^5 + y^5$?

  1. Srinivasa Ramanujan
  2. G. H. Hardy
  3. John Littlewood
  4. R. Tijdeman
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