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Always Perfect

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

perfect squares

$2 \times3 \times4 \times5 + 1 = 11^2$
$21 \times22 \times23 \times24 + 1 = 505^2$

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