Candido's identity, named after the Italian mathematician Giacomo Candido, states that for any two real numbers x and y, the square of the sum of x squared, y squared and the square of x plus y equals twice the sum of x to the fourth power, y to the fourth power and the fourth power of x plus y, an identity that in fact holds in every commutative ring rather than only for real numbers. Candido originally devised it to prove a matching identity for three consecutive Fibonacci numbers.
Facts
Classification
Statement Form Statement[x2 + y2 + (x+y)2]2 = 2[x4 + y4 + (x+y)4] 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Candido's identity (Wikipedia)
StatementQuote, Statement
[x² + y² + (x+y)²]² = 2[x⁴ + y⁴ + (x+y)⁴]
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