NRICH: Always Perfect

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

2×3×4×5+1=112
21×22×23×24+1=5052

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

Age 14 to 16


Algebra & Pre-Algebra, Quadratic Equations
High School, Educator

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NRICH (University of Cambridge)

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