Stage: 4 Challenge Level: 
$2 \times3 \times4 \times5 + 1 = 11^2$
$21 \times22 \times23 \times24 + 1 = 505^2$
Show that if you add $1$ to the product of four consecutive numbers the answer is ALWAYS a perfect square.
Factorisation (algebraic). Inequality/inequalities. Integers. Stage 5 - Reviewed 2012. Patterned numbers. Number theory. smartphone. Mathematical reasoning & proof. Manipulating algebraic expressions/formulae. Generalising.
Published January 2004.
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