Exercise · ZW-SUM-OF-TWO-SQUARES-004 · ★☆☆ Basic
What is the first prime of the form \(4k+1\)?
Choose one option.
Show answer
- C. 5
Explanation
The primes 3, 7, and 11 leave remainder 3 upon division by 4, while \(5\) leaves remainder 1.
Review the concept: Sum of two squares
An integer \(n\) is a sum of two squares if it can be written as the sum of the squares of two integers.
\[n = x^{2} + y^{2}\]
More practice problems: sum of two squares
- ZW-SUM-OF-TWO-SQUARES-001 According to Fermat's criterion, when is an odd prime p a sum of two squares?
- ZW-SUM-OF-TWO-SQUARES-002 Which of these equalities is correct?
- ZW-SUM-OF-TWO-SQUARES-003 Which of these numbers is NOT a sum of two squares?
- ZW-SUM-OF-TWO-SQUARES-005 Is the number 2 a sum of two squares?
- ZW-SUM-OF-TWO-SQUARES-006 Decide whether 37 is a sum of two squares using Fermat's criterion.
- ZW-SUM-OF-TWO-SQUARES-007 Is 65 a sum of two squares?
- ZW-SUM-OF-TWO-SQUARES-008 Is 63 a sum of two squares? (Recall that 63 = 3^2 · 7.)
- ZW-SUM-OF-TWO-SQUARES-009 Let n = 2 · 5^2 · 11. Is n a sum of two squares?