If a prime number on division by 4 gives a remainder of 1, then that number can be expressed as:
Options:
(A) sum of squares of two natural numbers
(B) sum of cubes of two natural numbers
(C) sum of square roots of two natural numbers
(D) sum of cube roots of two natural numbers
Official Answer Key:
A
Step-by-Step Solution & Explanation
This is Fermat's theorem on sums of two squares: every prime p ≡ 1 (mod 4) can be written as the sum of two perfect squares (e.g., 5=1²+2², 13=2²+3²). Answer: A.
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