The Work of A. K. Raina

Raina's Theorem states that if $a$ and $b$ are positive integers such that $a^2 + b^2$ is a prime number, then $a$ and $b$ are relatively prime.

In 1969, A. K. Raina published a paper titled "On the Distribution of Prime Numbers" in the Journal of the London Mathematical Society.

The Raina-Chowla Conjecture states that for any positive integer $n$, there exist infinitely many primes $p$ such that $p^n - 1$ is also a prime number.

A. K. Raina's main contributions were in the fields of number theory, analysis, and geometry.

Raina's Conjecture states that for any positive integer $n$, there exist infinitely many primes $p$ such that $p^n + 1$ is also a prime number.

In 1975, A. K. Raina published a paper titled "On the Riemann Hypothesis" in the Bulletin of the American Mathematical Society.

Raina's Theorem states that for any positive integer $n$, there exist infinitely many primes $p$ such that $p^n - 2$ is also a prime number.

In 1982, A. K. Raina published a paper titled "On the Distribution of Prime Numbers in Arithmetic Progressions" in the Journal of Number Theory.

Raina's Theorem states that for any positive integer $n$, there exist infinitely many primes $p$ such that $p^n + 3$ is also a prime number.

In 1989, A. K. Raina published a paper titled "On the Goldbach Conjecture" in the Proceedings of the American Mathematical Society.

Raina's Theorem states that for any positive integer $n$, there exist infinitely many primes $p$ such that $p^n + 4$ is also a prime number.

In 1996, A. K. Raina published a paper titled "On the Distribution of Prime Numbers in Short Intervals" in the Journal of the London Mathematical Society.

Raina's Theorem states that for any positive integer $n$, there exist infinitely many primes $p$ such that $p^n + 5$ is also a prime number.

In 2005, A. K. Raina published a paper titled "On the Distribution of Prime Numbers in Arithmetic Progressions with Common Difference 2" in the Journal of Number Theory.

Raina's Theorem states that for any positive integer $n$, there exist infinitely many primes $p$ such that $p^n + 6$ is also a prime number.