06-19-2026, 02:05 PM
Summary
Joseph-Louis Lagrange's Four-Square Theorem states that every nonnegative integer can be expressed as the sum of four integer squares. For example, $31 = 25 + 4 + 1 + 1 = 5² + 2² + 1² + 1²$. First conjectured by Pierre de Fermat and proved by Lagrange in 1770, the theorem is a landmark result in number theory because it guarantees that four squares are always sufficient, no matter how large the number. It inspired further research into representations of numbers as sums of squares and helped lay the foundations for modern additive number theory.
ARTICLE
Joseph-Louis Lagrange's Four-Square Theorem states that every nonnegative integer can be expressed as the sum of four integer squares. For example, $31 = 25 + 4 + 1 + 1 = 5² + 2² + 1² + 1²$. First conjectured by Pierre de Fermat and proved by Lagrange in 1770, the theorem is a landmark result in number theory because it guarantees that four squares are always sufficient, no matter how large the number. It inspired further research into representations of numbers as sums of squares and helped lay the foundations for modern additive number theory.
ARTICLE
┌────────────────────────────────┐
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘