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A problem about product of even squares and odd cubes

Source: Austrian Mathematical Olympiad 1998, Part 2, D1, P2

June 29, 2011
geometry3D geometrynumber theory proposednumber theory

Problem Statement

Let QnQ_n be the product of the squares of even numbers less than or equal to nn and KnK_n equal to the product of cubes of odd numbers less than or equal to nn. What is the highest power of 9898, that a)QnQ_n, b) KnK_n or c) QnKnQ_nK_n divides? If one divides Q98K98Q_{98}K_{98} by the highest power of 9898, then one get a number NN. By which power-of-two number is NN still divisible?
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