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Q. The number $(49^{2}-4)(49^{3}-49)$ is divisible by_______

Principle of Mathematical Induction

Solution:

Given expression $= (49^{2} - 2^{2}) \times 49 (49^{2} - 1)$
$= 51 \times 47 \times 49 \times 50 \times 48$
$= 51 \times 50 \times 49 \times 48 \times 47$
is the product of five consecutive integers. Hence it is divisible by $5!$.